w 

I 


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•.•--..•  ,•    -    , 


THE  ELEMENTS   OF  METALLOGRAPHY 


THE  ELEMENTS 

OF 

METALLOGRAPHY 


BY 

DR.  RUDOLF   RUER 
H 

PRIVATDOJZENT    AT    THE   UNIVERSITY    OF   GOETTINGEN 


AUTHORIZED  TRANSLATION 

BY 

C.   H.   MATHEWSON,  PH.D. 

INSTRUCTOR    IN    CHEMISTRY    AND    METALLOGRAPHY    AT   THE 

SHEFFIELD    SCIENTIFIC    SCHOOL   OF 

YALE   UNIVERSITY 


FIRST  EDITION 

FIRST    THOUSAND 


NEW  YORK 

JOHN  WILEY  &  SONS 

LONDON:    CHAPMAN  &  HALL,  LIMITED 

1909 


COPTBIOHT,    1909, 
BY 

C.  H.   MATHEWSON 

rv       ^ 


Stanhope  press 

P.    H.  GILSOH     COMPANY 
BOSTON,     U.S'A. 


TO 

PROFESSOR   DR.  G.  TAMMANN 

IN 
GRATEFUL    TOKEN    OF    ESTEEM 


293199 


AUTHOE'S  PREFACE. 


OUR  knowledge  of  the  constitution  of  metallic  alloys  has 
advanced  surprisingly  within  the  last  few  years.  This  has  been 
brought  about  for  the  most  part  by  careful  study  of  solidification 
and  transformation  processes  and  by  application  of  the  doctrine  of 
heterogeneous  equilibrium  to  such  processes.  Thus,  a  recital  of 
the  methods  by  means  of  which  these  results  have  been  obtained, 
must  constantly  rest  on  the  basis  of  the  above  doctrine.  However, 
the  presentation  which  we  have  before  us  is  not  intended  for  the 
exclusive  use  of  such  readers  as  are  thoroughly  familiar  with  the 
principles  of  physical  chemistry,  but  rather  for  anyone  who  is 
conversant  with  the  fundamental  facts  of  experimental  chemistry 
and  physics.  It  does  not,  therefore,  presume  knowledge  of  the 
doctrine  of  equilibrium. 

For  the  above  reason,  I  have  deemed  it  necessary  at  the  outset 
to  repeatedly  point  out  how  the  so-called  fusion  diagram  originates 
in  the  collective  arrangement  of  evidence  furnished  by  the  individ- 
ual experiments,  in  order  that  its  exclusive  significance  as  a  con- 
cise and  lucid  summary  of  the  experimental  results  may  be  brought 
prominently  into  view.  I  have  accordingly  made  no  extended 
use  of  the  phase  rule.  When  this  is  adopted  as  a  basis  for  the 
discussion,  much  abridgment  is  of  course  possible.  On  the  other 
hand,  there  is  on  the  part  of  the  beginner  a  certain  disinclination 
to  use  the  phase  rule  —  not  without  good  reason  in  my  opinion, 
for  although  it  does,  indeed,  furnish  a  general  view  of  possible 
equilibria  and  a  means  for  their  classification,  it  is  less  serviceable 
as  a  key  to  the  understanding  of  individual  cases.  Finally,  it  did 
not  appear  advisable  to  consider  the  gas-phase,  since  this  scarcely 
possesses  any  practical  bearing  upon  the  problems  in  hand. 

It  will,  perhaps,  seem  to  many  that  the  space  devoted  to  theo- 
retical discussion  is  somewhat  too  great  when  compared  with  the 
actual  material  which  it  includes.  I  have  desired,  however,  to 
avoid  a  possible  contingency  that  the  reader  who  manifests  a  lively 
interest  in  the  topics  which  lie  before  us,  fail  to  master  eventual 

vii 


viii  PREFACE. 

difficulties,  and  thus  emerge  imperfectly  informed  on  the  subject. 
Included  material  which  is  not  essential  to  the  preservation  of 
continuity  is  distinguished  by  small  print,  or  collected  in  the  shape 
of  supplementary  matter  at  the  close  of  certain  chapters.  I  have 
presented  only  a  limited  number  of  examples,  i.e.,  such  as  seem 
of  service  in  illustrating  general  developments.  Those  which  are 
introduced  at  the  beginning  are  subjected  to  rather  detailed  treat- 
ment, and  are  for  the  most  part  chosen  from  work  which  has  been 
carried  out  in  the  Institute  for  Inorganic  Chemistry  at  Goettingen. 

In  the  practical  part  of  the  book,  I  have  described  at  length 
only  such  experimental  appointments  as  have  been  developed,  or 
are  in  use  at  this  Institute,  and  which,  therefore,  come  within 
range  of  my  own  experience.  Dimensions  and  sources  of  refer- 
ence relative  to  such  apparatus,  etc.,  as  are  not  generally  familiar 
have  been  appended. 

It  is  intended  that  this  text  shall  place  the  reader  in  a  position 
to  intelligently  follow  the  literature  which  pertains  to  the  subject, 
and,  in  any  specific  instance,  to  use  the  methods  which  are  depicted 
herein,  and  which  are  by  no  means  restricted  in  their  application 
to  METALLOGRAPHY,  in  the  solution  of  chemical  problems.  Two 
works  of  similar  title  exist  at  present  in  the  German  language. 
E.  HEYN'S  "  Die  Metallographie  im  Dienst  der  Huttenkunde  "  partic- 
ularly conforms  to  the  purpose  of  awakening  interest  in,  and  fur- 
thering the  understanding  of,  the  subject  in  metallurgical  circles. 
The  aim  of  the  other  work  " Einfuhrung  in  die  Metallographie"1 
by  Paul  Goerens  probably  corresponds  closely  to  that  of  the  pres- 
ent text,  although  this  author  embodies  a  somewhat  different 
course  of  procedure.  I  venture  to  hope  that  my  presentation  as 
well  may  win  a  certain  friendly  appreciation. 

My  entry  into  this  field  of  activity  has  been  chiefly  furthered  by 
Professor  Tammann,  and  in  the  preparation  of  this  text  I  have 
been  fortunate  in  the  possession  of  much  valuable  advice  from  this 
source.  I  take  the  liberty  at  this  time  of  giving  expression  to  my 
feeling  of  gratitude  for  his  ever  willing  assistance  in  terms  of  the 
preceding  dedication. 

Dr.  Fr.  Doerinckel  has  rendered  valuable  assistance  in  proof- 
reading. 

R.  RUER. 
GOETTINGEN,  July,  1907. 

1  English  translation  by  F.  IBBOTSON  (Longmans,  1908). 


TRANSLATOR'S  NOTE. 


PROBABLY  by  far  the  greater  number  of  those  who  are  accus- 
tomed to  deal  with  metal  and  alloy  problems  have  devoted  little 
or  no  attention  to  physical  chemistry  and,  while  scarcely  able  to 
repress  some  degree  of  interest  in  recent  scientific  developments 
under  the  head  of  METALLOGRAPHY,  have  felt  disinclined  to  under- 
take a  serious  study  of  these  new  ideas  and  methods  owing  to 
unfamiliarity  with  the  principles  of  physical  chemistry  which  are 
involved.  Dr.  Ruer's  book  should  prove  serviceable  to  this  class 
of  workers,  largely  because  he  has  made  a  worthy  effort  to  render 
a  detailed  and  clear  explanation  of  the  most  essential  scientific 
principles  underlying  the  subject. 

The  student  of  metallurgy  or  of  engineering  stands .  in  very 
much  the  same  position.  No  great  amount  of  time  can  be  spent 
in  acquiring  a  theoretical  foundation  for  this  class  of  work,  and 
yet  some  knowledge  of  general  deductions,  i.e.,  of  the  structural 
relations  in  alloy  mixtures,  is  highly  desirable.  There  can  be  no 
doubt  that  any  careful  reader  who  is  reasonably  well  informed 
on  general  chemistry  and  physics  will  readily  follow  the  discus- 
sion in  this  book  and  gain  a  reliable  conception  of  the  various 
conditions  which  may  be  encountered  when  metals  are  alloyed 
with  one  another. 

While  the  author  intended  that  this  book  should  serve  as  an 
introduction  to  the  subject  and  in  no  sense  as  a  handbook,  it  is 
certainly  true  that  many  readers,  after  becoming  generally 
familiar  with  the  text,  will  particularly  desire  the  presence  of 
some  reference  material,  so  that  their  own  special  interests  may 
be  served.  An  elaborate  addition  in  the  shape  of  a  catalogue  to 
all  investigations  in  this  field  would  require  much  space  and 
would  interfere  somewhat  with  the  author's  plan,  but  I  have 
appended  a  complete  list  of  references  to  binary  fusion  diagrams  of 
all  investigated  systems  composed  of  twenty- three  chosen  metals. 

iz 


X  TRANSLATOR'S  NOTE. 

These  include  all  of  the  metals  which  have  been  somewhat  exten- 
sively studied  in  the  present  connection.  The  references  are 
arranged  in  an  order  based  upon  the  periodic  system  —  from 
sodium  to  palladium.  All  possible  binary  combinations  embracing 
these  twenty-three  metals  are  listed,  but  those  which  have  not 
yet  been  investigated  are  placed  in  brackets.  The  reference  for 
any  chosen  pair  will  be  found  under  the  metal  listed  first. 

C.  H.  MATHEWSON. 
NEW  HAVEN,  June,  1909. 


CONTENTS. 


INTRODUCTION. 

PAGE 

GENERAL  CONCEPTION  AND  PURPOSE  OF  THERMAL  ANALYSIS xv 


PART   I.  — THEORY. 

Chapter  I :  One  Component  Systems  3 

§  1.   GRAPHICAL  REPRESENTATION 3 

§  2.   TRANSFORMATIONS  OF  A  PURE  SUBSTANCE 6 

§  3.   COOLING-  AND  HEATING-CURVES   OF  PURE   SUBSTANCES   IN 

THE  ABSENCE  OF  TRANSFORMATIONS 11 

§  4.   COOLING-  AND  HEATING-CURVES  OF  PURE  SUBSTANCES  IN  THE 

PRESENCE  OF  TRANSFORMATIONS 17 

Chapter  II :  Heterogeneous  Equilibria 25 

Chapter  III :  Two  Component  Systems 37 

MUTUAL  SOLUBILITY  AND  STATE  OF  AGGREGATION 37 

§  1.   THE  LIQUID  STATE  is  CHARACTERIZED  BY  COMPLETE  Mis- 
CIBILITY;  THE  CRYSTALLINE  STATE  BY  COMPLETE  IMMISCI- 

BILITY 38 

THE  LAW  OF  FREEZING-POINT  LOWERING 38 

A.  Polymorphous    Transformations   do    not   Occur.     The   Com- 

ponents do  not  Unite  to  Form  a  Chemical  Compound 38 

1.  The  Crystallization  of  Aqueous  Solutions  of  Common  Salt .       38 

2.  Quantitative  Relations  on  Disintegration  into  Two  Phases 

(The  Lever  Relation) 54 

3.  General  Case 56 

4    Antimony-Lead  Alloys 72 

B.  Polymorphous  Transformations  do  not  Occur.     The  Compo- 

nents when  Fused  in  Conjunction  Unite  to  Form  One  or  More 

Chemical  Compounds  which  Melt  without  Decomposition.  .  75 

1.  General  Case 75 

2.  Magnesium-Tin  Alloys 89 

3.  Magnesium-Bismuth  Alloys 103 

xi 


xii  CONTENTS. 

PAGE 

C.  Polymorphous  Transformations  do  not  Occur.     The  Compo- 

nents when  used  in  Conjunction  Unite  to  Form  a  Chemical 
Compound  which  does  not  Melt  Unchanged,  but  Decomposes 
to  Melt  and  a  Second  Crystalline  Variety  on  Heating  (Case 

of  the  Concealed  Maximum) 107 

1.  Fusion  of  Glauber's  Salt,  Na2SO4-10  H20 107 

2.  General  Case 113 

3.  Sodium-Bismuth  Alloys 125 

4.  Gold- Antimony  Alloys 129 

5.  Incomplete  Progress  of  the  Decomposition 134 

D.  Changes  in  the  Crystalline  State 143 

§  2.  THE  LIQUID  STATE  is  CHARACTERIZED  BY  INCOMPLETE  Mis- 
CIBILITY;  THE  CRYSTALLINE  STATE  BY  COMPLETE  IMMISCI- 
BILITY 149 

A.  The  Components  do  not  Unite  to  Form  a  Chemical  Compound     153 

B.  The  Components  Unite  to  Form  a  Chemical  Compound 160 

§  3.   BOTH  THE  LIQUID  AND  CRYSTALLINE  STATES  ARE  CHARACTER- 
IZED BY  COMPLETE  MISCIBILITY 162 

GIBE'S  PRINCIPLE 165 

A.  Throughout  all   Concentrations  the  Separated  Crystals  Differ 

in  Composition  from  the  Melt  with  which  they  are  in  Equilib- 
rium. Type  I  according  to  Roozeboom 167 

B.  At  Given  Concentrations  the  Separated  Crystals  Possess  the 

Same  Composition  as  the  Melt  with  which  they  are  in  Equi- 
librium    182 

1.  The  Fusion  Curve  Possesses  a  Single  Maximum.     Type  II 

according  to  Roozeboom 182 

2.  The  Fusion  Curve  Possesses  a  Single  Minimum.     Type  III 

according  to  Roozeboom 185 

3.  The  Fusion  Curve  Possesses  a  Single  Horizontal  Inflex- 

ional Tangent 186 

4.  More  Complicated  Forms  of  the  Fusion  Curve 187 

C.  Horizontal   Course  of  the  Fusion  Curve   through  a    Finite 

Concentration  Interval 189 

D.  Polymorphous  Transformations 190 

E.  The  Components  Unite  to  Form  a  Chemical  Compound 192 

1.  The  System:  Bromine-Iodine 193 

2.  Magnesium-Cadmium  Alloys 195 

§  4.   THE  LIQUID  STATE  is  CHARACTERIZED  BY  COMPLETE  MISCIBIL- 
ITY;  THE  CRYSTALLINE  STATE    BY  INCOMPLETE    MISCIBIL- 
ITY    196 


CONTENTS.  xiii 

PAGE 

A.  Type  IV  according  to  Roozeboom 201 

B.  Type  V  according  to  Roozeboom 208 

C.  Polymorphous  Transformations 215 

D.  The  Components  Unite  to  Form  a  Chemical  Compound 218 

§  5.   THE  LIQUID  STATE  is  CHARACTERIZED  BY  INCOMPLETE  Mis- 

CIBILITY ;    THE  CRYSTALLINE  STATE  BY  COMPLETE  OR  INCOM- 
PLETE   MlSCIBILITY 222 

§  6.   THE  SEPARATION  OF  CRYSTALLINE  VARIETIES    WHICH  ARE 

NOT  COMPLETELY  STABLE 223 

A.  The  System:  Antimony-Cadmium 223 

B.  The  System:  Iron-Carbon 226 

1.  The  Incompletely  Stable  System:   Iron-Carbon 227 

2.  The  Completely  Stable  System:   Iron-Carbon 231 

3.  The  Complete  System:   Iron-Carbon 234 

§  7.   SUPPLEMENTARY 238 

A.  Methods  of  Determination  of  Equilibrium  Curves 238 

1.  Method  of  Solubility  Determination 238 

2.  Dilatometrical  Methods 239 

3.  Optical  Methods 240 

4.  Other  Methods 240 

B.  Methods  of  Investigation  of  Solidijied  Mixtures 241 

1.  Determination  of  the  Specific  Volume  of  the  Completely 

Solidified  Alloy 241 

2.  Determination  of  Electrical  Conductivity 242 

3.  Determination  of  the  Temperature  Coefficient  of  Electrical 

Conductivity 249 

4.  Determination  of  the  Vapor  Pressure  of  a  Component 252 

5.  Determination  of  the  Solubility  of  a  Component 263 

6.  Determination  of  Electrolytic  Solution  Tension 263 

7.  Determination  of  Heat  of  Formation 266 

8.  The  Method  of  Analysis  of  Residues 266 

Chapter  IV :  Three  Component  Systems 267 

§  1.   THE  LIQUID  STATE  is   CHARACTERIZED  BY  COMPLETE  MISCI- 

BILITY ;    THE  CRYSTALLINE  STATE  BY  COMPLETE  IMMISCIBIL- 

ITY 269 

A.  The  Components  do  not  Unite  to  Form  a  Chemical  Compound  269 

B.  The  Components  when  Fused  in  Conjunction  Unite  to  Form  a 

Chemical  Compound  which  Melts  without  Decomposition ...  275 

§  2.   BOTH  THE  LIQUID  AND  CRYSTALLINE  STATES  ARE  CHARACTER- 
IZED BY  COMPLETE  MISCIBILITY 277 

§  3.   SUPPLEMENTARY.     THE  PHASE  RULE 278 


Xiv  CONTENTS. 

PART   II.  — PRACTICE. 

PAGE 

Chapter  I :  Thermal  Investigation 289 

§  1.   MEASUREMENT  OP  TEMPERATURE 289 

§  2.   HEATING  APPARATUS    FOR    THE    PREPARATION  OP    FUSED 

ALLOYS 298 

A.  Far  Temperatures  up  to  1100° 298 

B.  For  All  Temperatures 299 

•C.  For  Temperatures  up  to  800°  and  1100°,  Respectively ,  in  a 

Protective  Atmosphere 303 

§  3.   DETERMINATION  OF  COOLING  CURVES  AND  HEATING  CURVES, 

RESPECTIVELY 304 

§  4.  CONSTRUCTION  OF  IDEALIZED  COOLING  CURVES  AND  HEATING 

CURVES,  RESPECTIVELY 306 

Chapter  II:  Investigation  of  Structure 316 

§  1.   PREPARATION  OF  SECTIONS 316 

§  2.   DEVELOPMENT  OF  STRUCTURE 319 

§  3.  MICROSCOPICAL  INVESTIGATION 323 

§  4.   PHOTOGRAPHY 325 

CONCLUSION 327 

COLLECTION  OF  REFERENCES  TO  BINARY  FUSION  DIAGRAMS 329 

INDEX  OF  AUTHORS'  NAMES 337 

INDEX  OF  SUBJECTS 339 


INTRODUCTION. 


GENERAL  CONCEPTION  AND  PURPOSE  OF  THERMAL  ANALYSIS. 

METALLOGRAPHY  deals  with  the  constitution  of  metallic  alloys 
and  with  the  methods  which  are  employed  in  the  investigation  of 
such  constitution. 

Solidified  metals  and  alloys  are  crystalline  in  their  general  make- 
up. The  crystallization  of  an  aqueous  solution  and  the  solidification 
of  a  molten  alloy  are  completely  analogous  processes.  Never- 
theless, owing  to  the  widely  different  temperatures  at  which  these 
respective  processes  are  realized,  it  is  not  feasible  to  extend  the 
well-known  methods  of  investigating  crystallization  processes  in 
aqueous  solution  to  analogous  processes  in  alloy  mixtures. 
Direct  observations  on  the  deposition  of  crystals,  and  separation 
of  these  crystals  from  the  mother  liquor  for  purposes  of  chemical 
analysis,  constitute  operations  which  are  incapable  (or  only  with 
extreme  difficulty  capable)  of  realization  in  a  metallic  alloy  — pre- 
sumably in  a  condition  of  red  heat  at  its  freezing  point.  We  are, 
then,  led  first  of  all  to  investigate  the  completely  solidified  alloy. 
However,  information  developed  on  these  grounds  must,  from  the 
very  nature  of  things,  be  incomplete.  For  this  reason,  much 
energy  has  been  expended  in  searching  for  methods  by  means  of 
which  the  same  degree  of  accuracy  can  be  obtained  in  interpreting 
crystallization  processes  in  a  white-hot  molten  material  and  ascer- 
taining the  composition  of  crystals  and  residual  mother  liquor, 
as  has  long  been  possible  with  the  older  methods  in  the  case  of 
aqueous  solutions. 

The  desired  end  has  been  attained  by  systematically  analyzing 
certain  phenomena  which  attend  crystallization.  As  such,  we 
may  cite  the  volume  change  to  which  a  melt  is  subject  during 
crystallization.  Again,  the  change  in  heat  content  which  is 
associated  with  change  in  state  of  aggregation  may  serve  the 
same  purpose.  This  latter  method  is  particularly  suited  to  the 

xv 


XVI  INTRODUCTION. 

matter  in  hand,  since,  in  the  observation  of  rate  of  cooling  or  rate 
of  heating  of  a  substance,  we  possess  a  very  convenient  means  of 
securing  an  approximate  estimate  of  the  differences  in  its  heat 
content  at  various  temperatures.  The  method  under  considera- 
tion, which  has  been  designated  "thermal  analysis"  by  TAMMANN, 
will  be  presented  in  detail  in  the  following  pages. 

It  follows  from  the  above  that  the  application  of  this  method 
is  not  restricted  to  the  investigation  of  metallic  alloys,  but  that 
the  selfsame  method  serves  as  well  in  the  general  study  of  crystalli- 
zation processes  in  a  melt  of  any  kind.1  Thus,  it  is  of  importance 
to  inorganic  chemistry.  It  finds  further  application  in  the  fields 
of  mineralogy  and  geology,  as  regards  the  constitution  of  rocks 
and  minerals  which  have  been  formed  on  crystallization  from  the 
molten  magma.  In  this  connection,  the  investigations  of  DoELTER,2 
VoGT,3  DAY  AND  ALLEN/  and  RINNE  5  may  be  mentioned.  Never- 
theless, metallic  alloys,  on  account  of  their  good  heat  conductivity 
and  their  particular  capacity  for  crystallization,  offer  the  least 
experimental  difficulty  in  the  application  of  this  method,  and  are, 
therefore,  excellent  objects  to  serve  by  way  of  its  further  develop- 
ment. 

1  C/.,  e.g.,  HEYN,  Copper  and  Cuprous  Oxide,  Contributions  from  the 
Royal  Technical  Experiment  Station,  Berlin,  315  (1900) ;  RUER,  Lead  Oxychlo- 
rides,  Z.  anorg.  Chem.,  49,  365  (1906);  PLATO,  Z.  phys.  Chem.,  58,  350  (1907). 

2  Cf.  here,  DOELTER,  Physico-chemical  Mineralogy,  Leipzig  (1905). 

3  VOGT,  Fused  Silicate  Solutions,  Christiania  (1903). 

4  DAY  and  ALLEN,  Z.  phys.  Chem.,  54,  1  (1906). 

J  RINNE,  New  Year  Book  of  Mineralogy  (1905),  I,  122. 


PART  I. 
THEORY. 


THE  ELEMENTS  OF  METALLOGKAPHY. 


CHAPTER   I. 
ONE  COMPONENT  SYSTEMS. 

§  1.   GRAPHICAL  REPRESENTATION. 

ASSUMED  that  a  body  continually  changes  in  temperature  as  a 
result  of  varying  addition  and  abstraction  of  heat.  We  will 
proceed  to  follow  the  course  of  this  change  by  making  successive 
temperature  observations  at  the  end  of  small  time  intervals  — 
every  ten  seconds,  for  example. 

TABLE  I. 


Elapsed 
time  in 
seconds. 

Temperature 
in  degrees. 

Elapsed 
time  in 
seconds. 

Temperature 
in  degrees. 

Elapsed 
time  in 
seconds. 

Temperature 
in  degrees. 

0 

10 

70 

132 

140 

186 

10 

30 

80 

145 

150 

187 

20 

60 

90 

153 

160 

183 

30 

70 

100 

162 

170 

175 

40 

90 

110 

170 

180 

162 

50 

105 

120 

175 

190 

138 

60 

120 

130 

181 

200 

110 

The  results  of  these  measurements  may  be  recorded  in  a  table 
(see  Table  1).  The  time,  in  seconds,  which  has  elapsed  since  the 
beginning  of  observation  is  entered  in  the  first  column  of  this 
table,  and  the  temperature  in  degrees  corresponding  to  each  time 
measurement,  in  the  second  column.  We  are  in  a  position  to 
conclude  from  this  table  that  the  temperature  of  the  body  rises 
at  first  rapidly,  then  more  slowly,  and  thereupon  falls  at  a  rate 
which  is  at  first  moderate  and  subsequently  becomes  rapid.  If  the 
observations  have  been  made  at  the  end  of  vanishingly  small 
time  intervals,  the  temperature  of  the  body  may  be  calculated  for 

3 


4  THE  ELEMENTS  OF  METALLOGRAPHY. 

any  time  between  two  of  these  intervals.  Such  calculation  rests 
upon  an  assumption  that  the  temperature  varies  uniformly  at  all 
points  between  two  successive  intervals. 

Although  a  table  of  this  sort  furnishes  complete  information 
with  regard  to  the  temperature  condition  of  the  body  during  the 
period  of  observation,  it  is  devoid  of  all  pictorial  effect.  Graphical 
representation,  wherein  a  geometrical  picture  is  substituted  for 
the  table,  is  not  open  to  this  objection.  For  this  purpose,  we 
choose  a  right  angled  coordinate  system,  i.e.,  we  draw  two  straight 
lines  OM  and  ON  (Fig.  1)  in  the  plane  of  the  paper  (which  latter 


N 
80 

V 

1*0° 

1 

^      o 

iio 

w 

£___ 

X 

0 

A 

10      20      30  M 

Time  in  Seconds 

FIG.  1. 

may  be  the  common  form  of  coordinate  paper  found  on  the  market) 
meeting  at  right  angles  in  the  point  0.  This  point  is  called  the 
origin,  while  the  two  lines  are  named  the  axes  of  the  system :  OM, 
the  axis  of  abscissas,  and  ON,  the  axis  of  ordinates.  Starting 
from  the  point  0,  we  lay  off  a  number  of  equal  spaces  upon  the 
axis  of  abscissas  OM  to  represent  the  lapsed  time  in  units  of  ten 
seconds.  The  temperature  in  degrees  centigrade  is  represented  in 
analogous  manner  along  the  axis  of  ordinates.  To  any  point  X  in 
the  coordinate  system,  there  corresponds  a  certain  time,  measured 
by  the  distance  OA  (called  abscissa),  and  a  certain  temperature, 
measured  by  the  distance  OB  (ordinate).  These  distances  OA 
and  OB  are  obtained  by  dropping  perpendiculars  from  the  point  X 
to  the  axes  OM  and  OAT  respectively.  In  the  present  example, 
the  point  X  corresponds  to  a  time  of  21  seconds  and  a  temperature 
of  31  degrees. 

The  figures  of  Table  1  are  represented  graphically  in  the  above 
manner  in  Fig.  2.  Now  imagine  that  verticals  be  erected  upon  the 
axis  of  abscissas  at  ten-second  intervals  and  at  lengths  which  are 


ONE  COMPONENT  SYSTEMS. 


proportional  to  the  temperatures  observed  at  the  respective  time 
values.  The  end  points  of  such  imaginary  verticals  are  denoted 
by  crosses.  On  passing  a  continuous  curve  through  these  end 
points,  we  are  in  a  position  to  at  once  read  off  the  temperature 
which  the  body  possessed  at  any  time  between  two  values  for 


200 


100 


\s 


100  200  300 

Time  in  Seconds 

FlG.  2. 

which  actual  observations  were  made.  The  distance  of  any  point 
upon  the  curve  from  the  time  axis  represents  the  temperature, 
while  that  portion  of  the  axis  of  abscissas  marked  off  by  a  vertical 
dropped  from  this  point,  represents  the  corresponding  time 
value.  This  method  of  ascertaining  temperatures  which  have 
not  been  observed  directly  is  more  accurate  in  principle  than  the 
above-mentioned  process  of  calculation,  which  rests  upon  the 
assumption  that  change  in  temperature  be  uniform  throughout 
a  definite  time  interval;  a  condition  represented  geometrically  by 
a  straight  line,  instead  of  a  curve,  from  one  point  to  the  other. 
Obviously,  the  results  which  appear  in  such  a  continuous  curve 
may  be  duplicated  by  the  use  of  a  suitable  method  of  calculation, 
although  the  operation  is  not  equally  simple. 

The  chief  advantage  to  be  ascribed  to  graphical  representation 
consists  in  its  quality  of  rendering  the  prevailing  conditions 
broadly  apparent  at  a  glance.  Where  the  scale  may  be  chosen  at 
will,  experimental  results  can  be  reproduced  as  accurately  in  this 
manner  as  through  the  figures  of  a  table.  In  general,  the  choice  of 
a  scale  is  subject  to  certain  restriction  on  the  ground  of  practica- 
bility. For  this  reason,  both  methods  of  representation,  tabular 
and  graphical,  are  ordinarily  used;  the  former  in  accurately  repro- 
ducing experimental  results,  and  the  latter  in  securing  a  general 
systematic  view  of  the  whole  field. 


6  THE   ELEMENTS  OF  METALLOGRAPHY. 

We  shall  give  preference  to  graphical  representation  in  the 
following  pages  and  in  general  imagine  the  results,  which  are 
presumed  to  represent  observations  at  sufficiently  short  intervals, 
continuously  joined  by  a  curve,  without  notation  of  the  separate 
determinations.  This  has  been  done  in  the  last  half  of  Fig.  2. 

§  2.   TRANSFORMATIONS   OF  A  PURE  SUBSTANCE. 

We  have  learned  by  experience  that  a  pure  substance  may  in 
general  sustain  various  alterations  in  its  state  of  aggregation  with- 
out change  in  composition.  Thus,  water  changes  to  steam  on 
heating,  and  the  latter  condenses  again  to  water  on  cooling  —  or 
solidifies  to  ice  at  a  lower  temperature. 

At  this  point,  a  brief  discussion  of  the  heat  processes  which 
occur  during  change  in  the  state  of  aggregation  of  a  pure  substance, 
particularly  during  change  from  the  crystalline  into  the  liquid 
state  and  conversely,  seems  essential. 

In  common  with  TAMMANN1  we  shall  avoid  the  term  "solid" 
in  defining  a  state  of  aggregation,  since  its  meaning  is  not  suffi- 
ciently well  denned  for  purposes  of  classification.  This  term 
has  been  commonly  applied  to  the  crystalline  as  well  as  to  the 
amorphous  state  of  a  substance,  and  in  this  connection  implies 
that  the  individual  particles  of  substance  when  assembled  in 
either  of  these  states  offer  considerable  resistance  to  mutual 
displacement.  Now,  a  crystalline  material  is  especially  charac- 
terized by  properties  which  are  partly  directional  in  nature,  i.e., 
different  in  different  directions.  On  the  other  hand,  amorphous 
or  glassy  substances  possess  properties  which  are  identical  in 
all  directions;  such  substances  are  isotropic,  after  the  manner 
of  liquids  and  gases,2  and  are  consequently  more  closely  related 
to  the  latter  forms  than  to  crystalline  bodies.  We  are  at  liberty 
to  consider  amorphous  bodies  as  liquids  of  high  viscosity.  In 
corroboration  of  this  view,  we  find  that  an  amorphous  body 
changes  its  viscosity  continuously  on  heating,  passing  without 
discontinuity  from  a  glassy  liquid  to  a  mobile  one,  while  trans- 
formation of  a  crystalline  body  to  an  isotropic  liquid  is  discon- 

1  Cf.  TAMMANN,  Krystallisieren  und  Schmelzen,  Leipzig,  1903. 

2  "Liquid  crystals"  are  disregarded  above.     Admitting  their  existence  as 
proven,  we  should  be  obliged  to  distinguish  between  isotropic  and  crystalline 
liquids.     The  term  liquid  is  used  here  in  the  isotropic  sense  alone. 


ONE   COMPONENT    SYSTEMS.  7 

tinuous,  i.e.,  characterized  by  sudden  change  in  all  of  its 
significant  properties.  Continuous  transformation  in  the  latter 
case  has  never  been  observed,  and  is,  according  to  TAMMANN, 
inconceivable. 

A  considerable  number  of  pure  substances  are  capable  of  being 
transformed  from  the  crystalline  to  the  liquid  state  without  sus- 
taining chemical  alteration:  they  melt  without  decomposition. 
Other  substances  are  not  fusible  without  decomposition.  In  due 
course  of  time  we  shall  become  acquainted  with  instances  wherein 
a  crystalline  substance  when  heated  decomposes  to  melt  and  a 
new  crystalline  variety.  For  the  present,  no  attention  will  be 
devoted  to  such  substances  as  fuse  with  decomposition. 

When  a  pure  substance  melts,  the  process  occurs  at  a  definite 
temperature  which  we  call  the  melting  point.  Strictly  speaking, 
the  melting  point  depends  upon  the  external  pressure,  and,  in 
general,  increases  with  the  pressure;  two  substances  only  whose 
melting  points  are  lowered  by  pressure  are  known.  These  are 
water  (H20)  and  bismuth  (Bi).  The  change  in  melting  point 
with  pressure  is,  however,  very  inconsiderable;  in  no  known 
case  exceeding  0.03°  per  atmosphere.  In  metallographical 
investigations,  all  determinations  are  usually  carried  out  under 
a  pressure  of  one  atmosphere,  viz.,  in  vessels  which  com- 
municate freely  with  the  atmosphere,  and  such  changes  in 
melting  point  as  are  due  to  variations  in  atmospheric  pressure 
can  hardly  reach  a  thousandth  of  a  degree,  being  of  far  lesser 
consequence  than  the  errors  which  are  associated  with  ordinary 
temperature  determination.  We  shall,  therefore,  disregard  all 
such  changes.1 

In  order  to  transform  a  unit  weight  of  a  substance,  1  gram 
for  example,  from  the  crystalline  state  to  the  liquid  state,  it  is 
necessary  to  add  a  definite  quantity  of  heat.  This  heat  quantity 
is  called  the  latent  heat  of  fusion  (per  gram)  of  the  respective 
substance,  and  is  measured  in  calories  (cal.),  i.e.,  that  quantity 
of  heat  which  is  required  to  elevate  the  temperature  of  1  gram 
of  water  1  degree.2  When,  on  the  other  hand,  a  substance  is 
changed  from  the  liquid  state  to  the  crystalline  state,  this  occurs 

1  Atmospheric  pressure  is  regarded  in  the  present  sense  as  mechanical 
pressure  operating  upon  the  melt  from  without. 

3  Cf.  here  NERNST,  Theoretische  Chemie,  IV  Ed.,  p.  11. 


8  THE  ELEMENTS  OF  METALLOGRAPHY. 

at  a  temperature  which  is  identical  with  the  melting  point  (in 
the  absence  of  supercooling),  and  which  is  called  the  freezing 
point,  while  during  the  process  a  definite  quantity  of  heat,  equal 
to  the  latent  heat  of  fusion,  is  liberated.  This  heat  of  crystal- 
lization, or  of  solidification,  must  be  removed  from  the  body  in 
proportion  as  it  is  liberated,  in  order  that  the  process  of  crystal- 
lization may  continue.  If  heat  addition  or  heat  abstraction  is 
suspended,  the  previously  started  fusion  or  solidification  cannot 
proceed,  i.e.,  crystal  and  melt  are  capable  of  coexistence  for  any 
length  of  time  at  the  temperature  of  the  melting  point:  they  are 
both  " stable"  at  this  temperature. 

When  heat  from  without  is  added  to  a  crystalline  substance 
of  an  integral  nature,  and  one  which  melts  without  decomposi- 
tion, its  behavior  may  be  detailed  as  follows,  in  line  with  previous 
explanations.  First  of  all,  the  temperature  of  the  body  rises 
slowly  until  its  melting  point  is  reached.  We  know  from  expe- 
rience that  fusion  begins  at  this  temperature,  and  some  portion 
of  the  added  heat  will  of  necessity  be  utilized  in  transforming 
the  body  from  the  crystalline  state  to  the  liquid  state.  Just 
what  fraction  of  the  supply  this  actually  is,  cannot  be  stated 
a  priori.  The  process  of  fusion  might  require  a  certain  finite 
length  of  time  whereby  the  supply  of  heat  could  be  more  rapid 
than  the  ensuing  fusion.  On  the  other  hand,  the  rate  of  fusion 
might  be  so  rapid  that  the  rate  of  heat  supply,  even  though  great, 
would  be  inappreciable  in  comparison.  In  the  first  case,  we 
would  have  a  more  or  less  retarded  temperature  rise,  depending 
upon  the  relation  between  both  rates.  A  period  of  perfectly 
constant  temperature  during  fusion  could  be  expected  in  the 
latter  case  only.  It  is  this  latter  condition  which  is  experimen- 
tally realized.  The  rate  of  fusion  at  the  melting  point  is  so  great 
that  any  rate  of  heat  supply  which  may  be  attained  in  practice 
is  negligible  in  comparison.  Very  recent  observations  by  DAY 
and  ALLEN1  and  by  DoELTER2  on  feldspar  and  quartz  seem,  never- 
theless, to  indicate  that  superheating  may  be  associated  with 
these  particular  substances.  Still  we  are  abundantly  justified 
in  disregarding  this  evidence  when  considering  the  special  sub- 
ject of  metals  and  alloys,  in  view  of  the  fact  that  no  indication 

1  DAY  and  ALLEN,  Z.  phys.  Chem.,  54,  1  (1906). 
3  DOELTER,  Z.  fiir  Electrochemie,  12,  617  (1906). 


ONE  COMPONENT  SYSTEMS.  9 

of  similar  behavior  has  ever  developed  relative  to  these  substances, 
nor  is  such  to  be  expected  on  the  basis  of  general  experience. 
Thus,  the  temperature  of  our  body  will  remain  constant  at  its 
melting  point  until  the  last  crystal  has  melted;  then  only  can 
further  heat  addition  be  attended  by  temperature  elevation.  It 
is  clear  that  heating  experiments,  as  outlined  above,  are  adapted 
to  the  determination  of  melting  points. 

A  molten  material  will  behave  as  follows  on  being  allowed  to 
cool  (removal  of  heat)  below  its  point  of  solidification  (melting 
point).  At  first,  a  fall  in  temperature  follows  heat  abstraction. 
Experience  has  shown  that  crystallization  does  not  necessarily 
ensue  when  the  melting  point  is  reached.  Many  substances  may 
be  retained  in  a  liquid  or  amorphous-glassy  state  at  temperatures 
far  below  their  melting  points,  and  there  is  reason  to  suppose 
from  the  investigations  of  TAMMANN*  that  the  greater  number  of 
substances  could  be  obtained  in  the  glassy  condition  by  suffi- 
ciently rapid  cooling.  There  are  various  ways  of  preventing  the 
supercooling  of  a  substance.  In  many  cases,  mere  stirring  is 
efficient  in  this  respect.  When  this  fails,  however,  the  desired 
effect  may  almost  invariably  be  secured  by  introducing  a  small 
crystalline  fragment,  and  stirring  at  the  same  time  if  necessary.2 
It  should,  however,  be  noted  that  even  this  expedient  cannot  be 
depended  upon  to  increase  the  rate  of  crystallization  indefinitely. 
According  to  TAMMANN'S  investigations  (1.  c.,  from  p.  131),  the 
rate  at  which  a  liquid  or  an  amorphous  body  becomes  trans- 
formed to  the  crystalline  state  actually  depends  upon  the  follow- 
ing two  factors: 

(1)  the  number  of   crystallization   centers  (nuclei)  which   are 
formed  within  the  liquid  in  a  unit  time,  and  which  depends  upon 
the  temperature  to  a  pronounced  extent,  and 

(2)  the  linear  rate  of  crystallization,  i.e.,  the  rate,  measured 
in   millimeters   per   minute,   or   otherwise,   at   which  crystalline 
growth  proceeds  after  inception  at  some  point,  and  under  the 
assumption  of  sufficiently  rapid  heat  abstraction.     This  is  also 
essentially  a  function  of  temperature,  and,  in  addition,  varies 
enormously  with  the  substance. 

1  Kristallisieren  und  Schmelzen,  p.  155. 

2  The  efficacy  of  stirring  is  probably  due  to  uniform  distribution  of  small 
crystals  which  have  formed  in  cooler  portions  of  the  melt  —  on  the  surface 
for  example. 


10  THE  ELEMENTS  OF  METALLOGRAPHY. 

Now,  by  inoculation,  we  are  able  to  increase  the  number  of 
crystalline  nuclei  only;  the  linear  rate  of  crystallization  is  thereby 
unchanged.  If  the  linear  rate  of  crystallization  in  the  vicinity 
of  the  melting  point  is  very  small,  the  actual  rate  of  crystalli- 
zation may  remain  less  than  the  rate  of  heat  outflow  as  determined 
by  experimental  conditions,  in  spite  of  the  large  number  of  crys- 
talline nuclei  produced  by  inoculation  and  stirring.  In  such  case, 
a  more  or  less  retarded  fall  in  temperature,  instead  of  a  period  of 
constant  temperature,  will  be  observed  during  solidification. 

The  rate  of  crystallization  is  extremely  small  for  many  silicates. 
(We  have  noted  that  these  substances  give  evidence  of  possible 
superheating.)  This  condition  seriously  hinders  the  study  of 
their  constitution.  Metals  and  alloys  appear  more  favorably  in 
this  respect.  It  is  true  that  marked  supercooling  of  metallic 
melts  not  infrequently  occurs,  but  inoculation  and  stirring  inva- 
riably suffice  to  relieve  this  abnormality,  since  the  linear  rate 
of  crystallization  in  the  vicinity  of  the  melting  point  has  always 
been  found  sufficiently  rapid  in  these  cases  to  render  any  rate 
of  heat  outflow  which  may  ordinarily  be  attained  experimentally, 
negligible  in  comparison,  viz.,  incapable  of  the  above  disturbing 
effect.  Here,  as  well  as  in  the  rest  of  the  theoretical  discussion, 
we  shall  neglect  the  possibility  of  appearance  of  supercooling, 
and  shall  proceed  under  the  assumption  that  crystallization 
begins  as  soon  as  the  melt  has  cooled  to  the  melting  temperature, 
and  progresses  at  a  rate  which  is  considerable  in  comparison  with 
the  rate  of  heat  outflow.  It  is  commonly  said  in  such  a  case 
that  the  reaction  is  "regulated  by  the  flow  of  heat"  alone. 
Under  these  conditions,  the  heat  liberated  during  crystallization 
will  cause  the  temperature  to  remain  constant  at  the  melting 
point  until  the  last  drop  of  liquid  has  crystallized. 

Fusion  is  not  the  only  transformation  which  a  crystalline  sub- 
stance may  sustain  without  change  in  its  composition.  We 
refer  here  to  polymorphism,  i.e.,  the  capability  of  a  substance 
to  exist  in  various  crystalline  forms.  It  has  been  demonstrated 
through  investigations  by  O.  LEHMANN,  H.  LECHATELIER  and 
G.  TAMMANN  that  polymorphism  is  a  widespread  property  of 
substances  in  general.  Our  attention  shall  be  confined  to  such 
transformations  as  are  reversible  (enantiotropic,  according  to 
O.  LEHMANN).  The  term  reversible  is  applied  to  those  trans- 


ONE  COMPONENT  SYSTEMS.  11 

formations  which,  as  in  the  case  of  fusion  and  crystallization, 
proceed  in  the  one  direction  when  heat  is  added,  and  in  the  other 
(reverse)  direction  when  heat  is  abstracted.  Thus,  they  are  com- 
pletely analogous  to  the  fusion  and  crystallization  of  a  pure  substance. 
In  these  cases,  which,  as  a  matter  of  fact,  constitute  the  smaller 
part  of  observed  cases  of  polymorphism,  there  exists  a  perfectly 
definite  temperature  under  atmospheric  pressure,  the  so-called  trans- 
formation, or  transition,  temperature,  above  which  the  one  form 
is  capable  of  existence,  and  below  which  the  other  form  becomes 
stable.  Both  forms  may  exist  side  by  side  at  the  transforma- 
tion temperature  only.  The  crystalline  form  which  is  stable  at 
the  lower  temperature  is  always  designated  as  the  a  form;  the 
crystalline  form  stable  at  the  higher  temperature  as  the  /?  form. 
One  stable  at  a  still  higher  temperature  would  be  called  a  7-  form, 
etc.  Addition  of  a  definite  quantity  of  heat  is  necessary  in  order 
to  effect  transformation  of  a  unit  mass  of  material  from  the  a 
form  into  the  /?  form.  This  is  called  the  heat  of  transformation. 
Conversely,  the  same  quantity  of  heat  would  be  liberated  during 
transformation  of  the  ft  form  into  the  a  form  (on  cooling).  The 
heat  of  transformation  is  usually  less  than  the  heat  of  fusion, 
although  cases  are  known  in  which  the  reverse  is  true.  The 
most  conspicuous  example  of  this  is  lithium  sulphate.  Accord- 
ing to  HUTTNER  and  TAMMANN/  the  heat  of  transformation  is 
here  five  times  as  great  as  the  heat  of  fusion. 

A  period  of  constant  temperature  will  be  observed  at  the  trans- 
formation point  (transition  point)  on  heating  and  cooling  a  sub- 
stance which  undergoes  reversible  transformation,  just  as  in  the 
case  of  fusion  and  solidification,  and  this  characteristic  tempera- 
ture may  be  determined  in  the  same  manner,  i.e.,  by  cooling  and 
heating  experiments. 

§  3.   COOLING-  AND  HEATING-CURVES  OF  PURE  SUBSTANCES  IN 
THE  ABSENCE  OF  TRANSFORMATIONS. 

We  have  seen  that  transformations,  wherein  we  shall  understand 
changes  in  state  of  aggregation  as  well  as  (reversible)  polymor- 
phous transformations,  are  made  evident  through  certain  heat 
effects,  and  may  therefore  be  detected  by  observation  of  the 
behavior  of  a  body  on  heating  and  cooling. 

1  HUTTNER  and  TAMMANN,  Z.  anorg.  Chem.,  43,  220  (1905). 


12  THE  ELEMENTS  OF  METALLOGRAPHY. 

We  shall  first  endeavor  to  become  familiar  with  the  process  of 
cooling  for  a  pure  substance  in  the  absence  of  transformations. 
Suppose  we  are  dealing  with  a  solid  body,  a  piece  of  platinum  for 
example,  at  a  higher  temperature  than  its  surroundings.  It  is 
assumed  that  the  heat  conductivity  of  the  substance  is  so  large 
that  measurable  temperature  differences  between  the  interior 
and  the  surface  of  the  metal  cannot  develop.  Let  the  body  be 
situated  in  an  evacuated  chamber,  in  order  that  outflow  of  heat 
by  means  of  air  currents  be  avoided.  Moreover,  let  the  tempera- 
ture of  its  surroundings  be  constant.  According  to  NEWTON'S 
Law  of  Cooling,  which  is  in  accord  with  experimental  results  pro- 
vided temperature  differences  are  not  too  great,  and  which  we  may 
therefore  adopt  as  the  basis  of  our  considerations,  the  quantity  of 
heat  given  off  in  a  unit  time  is  proportional  to  the  prevailing 
excess  of  the  temperature  of  the  body  over  that  of  its  surroundings. 

If  the  temperature  of  the  body  at  a  certain  time  is  T,  and  that  of 
the  surroundings  is  constantly  TQ,  then  the  quantity  of  heat  given 
off  during  the  small  interval  of  time  z,  within  which  the  tempera- 
ture T  does  not  fall  appreciably,  is 

w  =  kz  (T  -  T0),  (1) 

where  k  represents  a  proportionality  factor  dependent  upon  the 
surface  configuration  of  the  body. 

We  may  define  w  in  another  manner.  In  effect,  addition  or 
abstraction  of  a  definite  quantity  of  heat  from  various  bodies 
causes  their  temperature  to  rise  or  fall,  respectively,  to  a  varying 
degree.  As  is  well  known,  we  designate  that  quantity  of  heat  in 
calories  which  must  be  added  to  1  gram  of  a  body  in  order  to 
elevate  its  temperature  1  degree  as  the  specific  heat  of  the  body. 
When  a  body  of  the  mass  m  and  the  specific  heat  c  has  cooled 
t  degrees,  it  will  have  given  off  the  heat  quantity, 

w  =  met.  (2) 

By  equating  both  values  we  obtain 

met  =kz  (T  -  T0), 
or 

z      me  °  * 


ONE  COMPONENT  SYSTEMS.  13 

Thus,  t  is  the  fall  in  temperature  of  the  body  during  the  small 
interval  of  time  z,  whence  the  quotient  -  =  v  signifies  the  rate  of 
cooling.  We  may,  therefore,  write  equation  (3)  in  the  form 

v  =  JL  (T  -  T9).  (3a) 

me 

Now,  the  mass  m  and  the  surface  configuration,  defined  by  k, 
are  constant  for  the  same  body,  while  the  specific  heat  of  a  solid 
body  may  be  considered  very  nearly  independent  of  the  tempera- 

k 

ture.     Thus,  we  replace  the  expression  —  by  a  single  constant  K 

me 

and  obtain 

v  =  K  (T  -  5T0),  (3b) 

i.e.,  the  rate  of  cooling  is  at  any  instant  proportional  to  the  pre- 
vailing excess  of  the  temperature  of  the  body  over  that  of  its 
surroundings. 

The  body  therefore  cools  most  rapidly  at  first,  when  its  tem- 
perature is  highest;  the  temperature  falls  throughout  the  same 
interval  of  time  less  rapidly  in  proportion  as  the  actual  temperature 
of  the  body  becomes  less,  and  approaches  the  temperature  of 
the  surroundings  asymptotically  (theoretically,  at  least),  i.e.,  it 
continually  approaches  the  latter  without  actually  reaching  it. 
Obviously,  the  temperature  excess  of  the  body  over  its  surround- 
ings will  have  become  so  small  after  a  certain  time  as  to  be 
incapable  of  detection  with  our  measuring  instruments. 

Fig.  3,  Curve  1  gives  the  theoretical  cooling  curve  of  a  body 
according  to  Newton's  Law.  Time  values  are  entered  along  the 
axis  of  abscissas,  and  temperature  values  along  the  axis  of  ordi- 
nates,  as  explained  in  §  1.  The  initial  temperature  is  placed  at 
1000  degrees;  the  temperature  of  the  surroundings,  also  called  the 
convergence  temperature,  at  0  degrees.  The  form  of  the  curve  is 
determined  by  the  factor  K,  according  to  equation  (3b).  Since 
the  rate  of  cooling  for  a  temperature  excess  of  1000  degrees  is 
assumed  to  be  50  degrees  in  10  seconds,  K  becomes  (using  degrees 
centigrade  and  10-second  intervals  in  a  unit  significance)  ^<y. 
Observing  that  TQ  =  0,  we  have 

v  =        T. 


14 


THE  ELEMENTS  OF  METALLOGRAPHY. 


Thus,  the  body  cools  50  degrees  in  10  seconds  at  1000  degrees, 
40  degrees  at  800  degrees,  10  degrees  at  200  degrees,  etc.,  as  may 
be  seen  from  Curve  1.  Such  a  curve  is  known  as  a  logarithmic 
curve. 

1000° 


900 
800° 


0° 


100      200       900     400       500      600      700 
Time  in  Seconds 

FIG.  3. 


800       900      1000 


Turning  once  again  to  the  first  form  of  equation  for  the  rate 
of  cooling,  viz.,  (3a), 

v  =  JL  (T  -  TQ), 
me 

we  shall  be  able  to  draw  certain  conclusions  relative  to  the  rates 
of  cooling  of  two  bodies  of  different  nature.  For  this  purpose, 
ail  consideration  of  the  surface  configuration  of  the  materials  — 
determining  the  factor  k  —  may  be  eliminated  by  placing  each 
substance  in  a  similar  vessel  of  thin,  polished  platinum  foil,  so 
that  each  attains  the  same  surface.  Moreover,  we  shall  assume 
the  use  of  equal  weights  of  the  different  substances  for  these 
comparative  experiments,  whence  ra  and  k  as  well,  become 
constant.  Let  the  specific  heats  of  the  two  substances,  again 


ONE  COMPONENT  SYSTEMS.  15 

regarded  as  independent  of  the  temperature,  be  ct  and  c2.  Now, 
if  T  —  T0  also  be  chosen  equal  for  both  bodies,  we  obtain 

s-t 

This  expression  signifies  that  the  rates  of  cooling  of  equal  weights 
of  two  bodies  are  inversely  proportional  to  their  specific  heats 
where  the  bodies  possess  the  same  surface  configuration  and  the 
same  temperature  excess  above  their  surroundings. 

It  is  clear  that  the  periods  of  cooling  are  determined  by  the 
rates  of  cooling.  We  readily  see  that  a  body  which  moves  at 
twice  the  rate  of  another  body  in  every  point  of  its  path  will 
traverse  a  given  distance  in  half  the  time  required  by  the  second 
body.  In  analogous  manner,  it  may  be  said  here  that  a  body 
which  possesses  twice  the  rate  of  cooling  of  another  body  at 
every  temperature  will  require  only  half  as  much  time  as  the 
latter  to  cool  through  the  same  temperature  interval.  Thus,  if 
we  designate  the  periods  which  two  bodies  with  the  respective 
rates  of  cooling  v^  and  v2  require  to  cool  off  to  the  same  extent, 
by  Zl  and  Z2,  we  obtain  the  relation 


i.e.,  the  periods  during  which  two  bodies  of  the  same  mass  and 
the  same  surface  configuration  will  cool  off  to  the  same  extent, 
where  their  temperature  excess  above  the  external  temperature 
is  the  same,  are  directly  proportional  to  their  specific  heats. 

This  result  is,  in  the  main,  apparent  without  extended  dis- 
cussion; that  body  which  possesses  the  greatest  specific  heat, 
i.e.,  which  possesses  the  greatest  heat  supply  per  unit  mass,  will 
require  the  most  time  to  give  up  this  heat  supply  to  its  sur- 
roundings, all  other  conditions  being  equal. 

Curve  II,  Fig.  3,  gives  the  theoretical  cooling  relations  for  a  body 
of  twice  the  specific  heat  represented  in  Curve  I,  the  initial  and 
convergence  temperatures,  as  well  as  the  quantity  of  material  and 
surface  configuration  being  the  same  in  both  cases.  We  observe 
that  Curve  II  is  much  flatter  than  Curve  I,  and  that  the  periods 
required  for  traversing  the  same  temperature  interval  are  twice 
as  long  upon  Curve  II  as  upon  Curve  I. 


16 


THE  ELEMENTS  OF  METALLOGRAPHY. 


DULONG  and  PETIT  used  the  relation  given  in  equation  (5)  in 
their  determination  of  specific  heat  and  discovery  of  the  well- 
known  law  relative  to  atomic  heats  which  bears  their  names. 
According  to  the  experiments  of  REGNAULT,  however,  the  accuracy 
of  this  method  is  not  very  great,  principally  for  the  reason  that 


100 


100  200  300  400  500  600  700  800  900  1000 
Time  in  Seconds 

FIG.  4. 


the  fundamental  requirement  of  sufficient  heat  conductivity  to 
preclude  the  occurrence  of  measurable  temperature  difference  in 
the  material  at  hand  is  not  even  approximately  realized  in  prac- 
tice, except  where  good  conducting  solid  bodies  and  liquids  are 
in  question. 

When  a  body  possessing  no  transformation  point  is  heated, 
conditions  which  are  completely  analogous  to  those  just  dis- 
cussed are  encountered.  The  temperature  rises  rapidly  at  first, 
then  more  slowly,  and  finally  approaches  an  upper  convergence 
temperature  asymptotically.  The  value  of  this  upper  converg- 
ence temperature  depends  upon  the  temperature  of  the  external 


ONE  COMPONENT  SYSTEMS.  17 

source  of  heat,  as  well  as  upon  the  nature  of  heat  insulation 
embodied  in  the  experimental  arrangement.  Fig.  4  gives  a  heat- 
ing curve  constructed  after  the  manner  of  the  cooling  curves 
already  discussed. 

§  4.   COOLING-  AND  HEATING-CURVES  OF   PURE    SUBSTANCES  IN 
THE  PRESENCE  OF  TRANSFORMATIONS. 

Attention  is  now  directed  to  cooling  and  heating  curves  of  a 
pure  substance  when  transformation  points  occur  within  the 
temperature  range  under  investigation.  First  of  all,  we  shall 
consider  a  single  transformation,  viz.,  transformation  from  the 
liquid  to  the  crystalline  state.  Suppose  we  are  dealing  with  a 
body  in  the  liquid  condition  at  1000  degrees,  which  solidifies 
to  a  crystalline  variety  at  a  definite  temperature,  e.g.,  at  650 
degrees.  Let  the  heat  conductivity  of  the  body  be  so  large  that 
no  measurable  differences  in  temperature  can  occur  within  the 
body  itself.  Let  there  be  no  question  of  supercooling.  Let  the 
vessel  containing  the  body  be  so  thin  that  its  mass,  and  therefore 
its  heat  capacity,  may  be  neglected  in  comparison  with  the  heat 
capacity  of  the  body.  Moreover,  let  the  vessel  be  situated  in 
an  evacuated  chamber.  As  in  the  preceding  examples,  let  the 
exterior  temperature  (convergence  temperature)  be  0  degrees. 
Finally,  we  make  an  assumption  that  our  experimental  apparatus 
is  so  constructed  that  the  rate  of  cooling  at  the  beginning  of 
the  experiment  (at  1000  degrees)  is  precisely  that  previously 
shown  in  Curve  I,  viz.,  50  degrees  in  10  seconds.  If  no  trans- 
formation should  occur,  the  complete  course  of  the  curve  would 
then  be  determined  by  the  formula  v  =  K  (T  —  T0);  it  would 
be  identical  with  that  given  by  Curve  I,  Fig.  3.  Crystallization 
begins  at  650  degrees,  and  we  may  assign  such  a  value  to  the 
heat  of  crystallization  which  is  liberated  at  this  point,  that  it 
compensates  the  loss  of  heat  from  the  body  to  its  surroundings 
for  200  seconds.  Suppose  that  the  last  drop  of  liquid  has  crys- 
tallized at  the  end  of  this  interval,  i.e.,  that  this  source  of  heat 
is  then  exhausted.  The  temperature  of  the  body  now  falls  again 
according  to  Newton's  Law  of  Cooling. 

According  to  the  above,  the  portion  ab  of  the  curve  (Fig.  5) 
must  be  identical  with  the  corresponding  portion  of  Curve  I,  Fig.  3. 


18 


THE  ELEMENTS  OF  METALLOGRAPHY. 


But  from  the  point  b  the  temperature  does  not  continue  to  fall 
in  accordance  with  the  dotted  continuation  of  ab',  it  remains 
constant  for  200  seconds.  The  horizontal  portion  be  of  the  cooling 
curve  corresponds  to  this  period  of  constant  temperature.  A 
period  of  this  sort  is  called  a  halting  point.  At  this  juncture,  it 
would  be  simplest  to  assume  that  further  cooling  below  c  proceeds 
just  as  though  no  transformation  had  taken  place.  Representing 
this  idea  geometrically,  we  would  displace  the  dotted  prolongation 
bb'  across  the  portion  be,  causing  it  to  continue  on  from  the  end 


1000°, 


900 


100  200  300  400  500  600  700  800  900  1000 
Time  in  Seconds 

FIG.  5. 


point  of  solidification  at  c  parallel  to  its  previous  course.  In  so 
doing,  however,  we  should  be  making  an  assumption  the  qualifi- 
cations of  which  cannot  be  settled  a  priori,  as  we  shall  proceed  to 
point  out.  Formula  (3a)  for  the  rate  of  cooling  (p.  13)  reads 


me 


ONE  COMPONENT  SYSTEMS. 


19 


That  portion  of  the  expression  which  determines  the  rate  of 
cooling  for  a  given  temperature  excess  above  the  surrounding  is 
seen  to  be 

A 
me 

Now,  the  mass  has  obviously  remained  constant,  and  the  same  is 
true  of  the  factor  k,  which  is  determined  by  the  surface  configura- 
tion, since  we  have  conducted  the  cooling  in  one  and  the  same 
vessel.  But  the  specific  heat  may  have  changed.  If  an  assump- 
tion that  the  dotted  curve  cc'\\bbf  represents  the  temperature 
condition  of  the  body  from  c  onwards  were  correct,  it  would 


1000 


900 


\ 


300       400       500       600 
Time  in  Seconds 

FIG.  6. 


700       800      900      1000 


signify  that  the  specific  heat  of  the  molten  body  had  not  changed 
during  transformation  into  the  crystalline  state.  This  is  contra- 
dicted, however,  by  common  experience.  It  is  quite  generally 
true  that  the  specific  heat  of  a  body  when  in  the  liquid  state  is 
greater  than  when  in  the  crystalline  state. 


20  THE  ELEMENTS  OF  METALLOGRAPHY. 

Thus,  the  specific  heat  after  solidification  is  here  greater  than 

Jc 

before.     Hence  the  expression —  >  signifying  the  rate  of  cooling  for 

VYIC 

a  given  temperature  difference,  is  greater  than  would  correspond 
to  a  parallel  displacement  of  the  curve  branch  W,  as  described. 
The  full  branch  cd,  which  is  intended  to  represent  the  true  course 
of  cooling,  gives  expression  to  this  decrease  in  specific  heat,  in 
that  it  falls  off  more  steeply  than  cc'.  A  25  per  cent  decrease  in 
specific  heat  is  assumed  in  its  construction. 

If,  in  addition  to  the  fusion,  polymorphous  transformation 
occurs  within  the  observed  temperature  interval,  whereby  a  second 
crystalline  variety  is  formed,  a  second  period  of  constant  tem- 
perature must  be  observed,  provided  the  heat  effect  of  this 
transformation  is  not  vanishingly  small.  A  modification  of  the 
preceding  temperature  changes  to  accord  with  the  occurrence 
of  an  additional  (polymorphous)  transformation  at  150  degrees 
is  given  in  Fig.  6.  The  halting  period  de  for  this  second  trans- 
formation is  also  placed  at  200  seconds.  Furthermore,  on  account 
of  simplicity,  the  specific  heats  of  the  crystalline  variety  stable 
at  the  higher  temperature  (/?  form)  and  that  stable  at  the  lower 
temperature  (a  form)  are  assumed  to  be  equal.  No  generalization 
in  this  respect,  as  was  cited  relative  to  the  specific  heats  of  a 
body  in  the  crystalline  and  liquid  states,  can  be  offered. 

We  are  in  no  wise  at  liberty  to  conclude  from  the  equal  lengths 
of  the  halting  points,  viz.,  the  distances  be  and  de,  that  the  heats 
of  fusion  and  transformation  are  equal.  However,  it  is  possible  to 
use  these  values  in  drawing  certain  conclusions  relative  to  the 
mutual  relation  of  both  heat  effects,  and  we  are  hereby1  possessed 
of  a  very  convenient  method  for  obtaining  an  approximate 
numerical  estimate  of  this  relation. 

This  may  be  seen  as  follows.  The  rate  of  cooling  signifies  the  fall  in 
temperature  during  a  unit  time: 

r-t- 

Z 

According  to  equation  (2),  p.  12,  the  heat  quantity  given  off  through- 
out the  temperature  fall  t  is  w  =  met,  where  m  represents  the  mass  of  the 
material  and  c  its  specific  heat.  Eliminating  t  by  using  the  above  equa- 
tion for  the  rate  of  cooling,  we  obtain  the  expression 

w  =  mcvz. 

and  TAMMANN,  Z.  anorg.  Chem.,  43,  218  (1905). 


ONE  COMPONENT  SYSTEMS.  21 

Thus,  w  is  the  quantity  of  heat  which  the  body  gives  up  to  the  surround- 
ings at  the  temperature  in  question,  during  the  fraction  of  time  z.  This 
would  cause  a  slight  fall  in  temperature  t.  Now,  if  a  fall  in  temperature 
is  prevented  through  the  agency  of  the  internal  heat  source,  which  yields 
heat  in  the  form  of  heat  of  fusion  or  of  transformation,  then  the  quantity 
of  heat  given  up  to  the  surroundings  during  every  fraction  of  time  z  must 
have  been  compensated  from  this  internal  source.  If,  then,  the  heat 
quantity  W,  which  has  been  liberated  during  the  time  Z,  has  served  to 
maintain  the  temperature  constant,  it  must  amount  to 

W  =  mcvZ. 

We  are  therefore  in  a  position  to  determine  the  relation  between  any 
two  liberated  heat  quantities  TFt  and  W2  by  using  the  cooling  curves  in 
connection  with  information  concerning  the  masses  and  specific  heats  of 
the  substances  in  question: 

W,  =  m^Z, 
W2      m2c2v2Z2 

Obviously,  if  the  actual  value  of  one  heat  quantity,  e.g.,  of  TF,,  is  known, 
the  value  of  the  other,  W2,  may  be  calculated  at  once. 

No  assumptions  relative  to  the  relation  between  rate  of  cooling  and 
temperature  were  made  during  the  above  discussion.  Formula  (1)  does 
not  therefore  presume  validity  of  Newton's  Law  of  Cooling. 

When  two  liberated  heat  quantities  are  compared  upon  the  same  cool- 
ing curve,  as  in  the  present  instance,  the  values  ml  and  m2  cancel  from 
the  formula,  and  we  have 


W2 

This  formula  appears  vague  in  one  respect.  We  have  seen  that  the 
specific  heat  of  a  substance  depends  upon  the  state  of  aggregation.  In 
the  construction  of  the  curve  given  in  Fig.  6,  for  example,  we  assumed  a 
falling  off  in  specific  heat  of  25  per  cent  on  solidification.  Some  doubt 
might  accordingly  arise  as  to  which  specific  heat  were  implied  by  the 
subscript  1  where  the  letters  bearing  this  subscript  refer  to  values  asso- 
ciated with  solidification.  The  question  is,  whether  the  specific  heat  of 
the  body  in  the  liquid  or  in  the  crystalline  state  should  be  substituted  in 
the  formula.  As  a  matter  of  fact,  it  makes  no  difference  which  is  chosen, 
as  long  as  the  corresponding  rate  of  cooling  is  used  at  the  same  time. 
According  to  equation  (4),  p.  15,  the  rates  of  cooling  are  inversely  pro- 
portional to  the  specific  heats,  for  the  same  temperature  excess  above  the 
surroundings,  and  similarity  of  other  conditions  (i.e.,  the  same  mass  and 
the  same  surface  configuration).  Differentiating  between  values  which 


22  THE  ELEMENTS  OF  METALLOGRAPHY. 

x 

apply  to  the  liquid  and  crystalline  states  by  the  indices  (')  and   ("), 
respectively  we  write, 


i.e.,  the  product  of  specific  heat  and  (corresponding)  rate  of  cooling  is 
constant.  We  may  thus  refer  both  values  vl  and  Ci  at  will  to  either  the 
liquid  or  crystalline  state  when  using  them  in  formula  (2),  as  follows: 

&_&&{ 

W,  -    c^Z,  ' 
or, 

W       c"v"Z" 
W,  =  ^A~ 

Now,  at  this  point  we  observe  that  the  specific  heats  of  solid  bodies 
are  independent  of  the  temperature  within  rather  wide  limits,  provided 
no  polymorphous  transformations  occur.  Therefore,  choosing  formula 
(2b),  in  which  the  rate  of  cooling  v"  and  the  specific  heat  c"  refer  to  the 
material  after  solidification  (along  be,  Fig.  6,  in  the  present  case)  we 
reflect  that  c"  at  650  degrees  must  invariably  approximate  the  specific 
heat  of  the  body  at  150  degrees,  before  transformation,  and  make  the 
change, 


or,  considering  the  possibility  of  change  in  specific  heat  during  polymor- 
phous transformation, 

S-S- 

In  this  formula,  Wv  represents  the  heat  of  fusion,  TF2  the  heat  of  trans- 
formation, Zi  and  Z2  the  duration  of  the  respective  halting  points,  v,'' 
the  rate  of  cooling  at  the  melting  temperature  after  crystallization,  and 
v/  the  rate  of  cooling  at  the  temperature  of  polymorphous  transforma- 
tion before  the  change. 

Only  such  values  are  contained  in  formula  (3)  as  may  be  read  directly 
from  the  cooling  curves  —  knowledge  of  specific  heats  is  not  required  in 
its  use. 

In  the  previous  example,  (Fig.  6),  Zt  =  Z2  =  200  seconds,  v/'  =  43 
degrees  in  10  seconds,  and  v2f  =  10  degrees  in  10  seconds,  whence  the 

W 
relation  —  '  gives  the  value  4.3,  i.e.,  the  heat  of  fusion  is  4.3  times  the  heat 

of  polymorphous  transformation. 

For  the  purpose  of  simplifying  the  above  considerations,  we  assumed 
perfect  heat  conductivity  of  the  substances,  non-appearance  of  super- 


ONE  COMPONENT  SYSTEMS. 


23 


cooling,  and  cooling  in  an  evacuated  chamber  towards  an  invariable 
convergence  temperature.  These  assumptions  are  not  perfectly  realized 
in  practice.  It  will  be  shown  in  Part  II,  Practice,  that  v  is  not  constant 
along  the  halting  points  of  cooling  curves  obtained  under  usual  conditions. 
Moreover,  it  is  scarcely  possible  to  exceed  an  accuracy  of  10  per  cent  in 
the  determination  of  halting-point  periods,  since  a  difference  as  large  as 


1000 


100    SOO    300    400     500     600    700    800    900    1000 
Time  in  Seconds 
FIG.  7. 

this  frequently  characterizes  the  results  from  two  experiments  carried 
out  under  precisely  the  same  conditions.  Consequently,  this  method 
amounts  to  little  more  than  an  extremely  convenient  and  simple  means 
of  estimating  results.1 

When  a  source  of  uniform  heat  supply  is  used  in  elevating  the 
temperature  of  a  body,  the  resulting  heating  curve  reveals  any 
transformation  points  which  may  exist,  after  the  manner  of  a 
cooling  curve.  The  temperature  rises  continuously  (Fig.  7)  up 
to  the  transformation  point  in  question,  when  a  period  of  constant 

1  Compare  PLATO  relative  to  changes  in  cooling  conditions,  Z.  Phys. 
Chem.,  55,  721  (1906). 


24  THE  ELEMENTS  OF  METALLOGRAPHY. 

temperature  is  observed.  After  transformation  has  become  com- 
plete, a  second  rise  of  temperature  ensues.  This  culminates  in 
the  second  transformation  point,  here  the  melting  point,  where  a 
second  period  of  constant  temperature  is  observed.  After  com- 
plete fusion,  the  temperature  rises  for  a  third  time,  in  this  case, 
assymptotically  towards  1000  degrees  as  an  upper  limit.  The 
heating  curve  is  of  certain  practical  importance  in  checking  the 
cooling  curve.  Of  particular  significance  in  this  connection  is 
the  fact  that  the  exceedingly  inconvenient  phenomena  of  super- 
cooling which  frequently  appear  upon  the  cooling  curve  find  no 
counterpart  upon  the  heating  curve  in  the  form  of  superheating, 
provided  pure  substances  only  are  under  investigation.  We  shall 
return  to  this  subject  later  on  in  the  second  part  of  the  book.  As 
far  as  the  ensuing  discussion  is  concerned,  since  it  embodies  an 
assumption  of  theoretically  normal  cooling  curves  in  the  interest 
of  simplicity,  no  attention  need  be  devoted  to  any  other  modified 
curves. 


CHAPTER  II. 
HETEROGENEOUS  EQUILIBRIUM. 

IN  this  chapter  we  shall  discuss  certain  laws  of  chemical  statics, 
familiarity  with  which  will  be  of  value  in  furthering  a  satisfactory 
understanding  of  what  is  to  follow. 

In  every  investigation  it  is  essential  that  the  object  under 
examination  be  protected  from  uncontrollable  influences  on  the 
part  of  its  surroundings.  We  shall  designate  those  objects  of 
investigation  which  may  be  considered  immune  from  certain 
external  influences,  such  as  a  flow  of  energy  in  either  direction, 
and  which  may,  therefore,  be  regarded  as  isolated  in  this  sense,  as 
closed  systems,  or,  in  a  word,  systems. 

We  differentiate  between  such  systems  as  are  homogeneous  and 
such  as  are  heterogeneous.  A  system  is  said  to  be  homogeneous 
when  it  possesses  the  same  physical  and  chemical  properties  in  its 
every  part,  as  far  as  any  division  may  be  affected  by  mechanical 
means;  otherwise  it  is  said  to  be  heterogeneous.  Thus,  a  gas,  a 
liquid,  or  a  single  crystalline  variety  constitutes  a  homogeneous 
system,  while  a  system  composed  of  a  gas  and  a  liquid,  or  of  two 
immiscible  liquids,  or  of  two  or  more  crystalline  varieties,  etc., 
must  be  characterized  as  heterogeneous.  Hence  it  appears  that 
a  heterogeneous  system  may  be  regarded  as  composed  of  two 
or  more  homogeneous  systems.  According  to  WILLARD  GiBBS1 
the  originator  of  the  doctrine  of  heterogeneous  equilibrium,  the 
homogeneous  systems  which  compose  an  heterogeneous  system 
are  called  phases.  Thus,  an  homogeneous  system  is  composed 
of  a  single  phase,  while  an  heterogeneous  system  is  composed  of 
at  least  two  phases. 

If  a  system  sustains  no  alteration  on  being  left  to  itself  for  an 
indefinite  length  of  time,  we  say  that  it  is  in  equilibrium.  Theo- 
retically this  is  an  adequate  criterion,  but  practically  it  may  lead 
to  error  in  certain  instances,  namely,  when  the  reaction  velocity 

1  WILLARD  GIBBS,  Studies  in  Thermodynamics,  Trans.  Conn.  Acad.,  iii, 

1875-8. 

25 


26  THE  ELEMENTS  OF  METALLOGRAPHY. 

of  the  substances  concerned  is  exceedingly  small.  By  way  of 
example,  the  well-known  case  of  hydrogen  and  oxygen  may  be 
cited.  A  mixture  of  these  substances  may  be  kept  for  years  at 
ordinary  temperature  without  change.  But  it  is  merely  necessary 
to  heat  the  mixture  sufficiently  high  at  a  single  point  for  an 
instant  —  viz.,  by  means  of  an  electric  spark  —  in  order  to  bring 
about  an  unusually  violent  combination  of  the  two  gases  in  any 
quantity,  provided  the  proper  proportions  are  observed  in  the 
mixture.  On  the  other  hand,  we  are  well  aware  that  it  is  impos- 
sible to  induce  an  automatically  progressive  decomposition  of 
water  into  hydrogen  and  oxygen  by  momentarily  subjecting 
water  or  steam  to  a  high  temperature.  Hence,  we  conclude 
that  a  mixture  of  hydrogen  and  oxygen  is  not  in  a  condition  of 
equilibrium,  and  our  experience  relative  to  reaction  velocity  in 
general  justifies  the  assumption  that  water  is  formed  from  the 
mixture  even  at  ordinary  temperature;  so  slowly,  however,  that 
the  quantity  produced  in  years  cannot  be  detected  with  our 
available  measuring  instruments. 

Now,  there  can  be  no  doubt  that  equilibrium  obtains  wherever 
a  process  is  reversible.  Thus,  if  we  observe  that  a  closed  system 
composed  of  a  single  crystalline  variety  and  its  melt  suffers  no 
change  in  the  quantity  of  either  constituent,  we  may  convince 
ourselves  in  a  very  simple  manner,  owing  to  the  reversibility 
of  the  process  (crystallization  and  fusion)  that  equilibrium  is 
actually  at  hand.  For,  if,  on  supplying  heat  to  the  system,  a 
decrease  in  the  quantity  of  crystals,  and,  on  abstracting  heat, 
an  increase  in  the  quantity  of  crystals,  is  observed,  the  invaria- 
bility of  our  system  could  not  have  been  due  to  a  too  trifling 
rate  of  reaction.  The  system  is  rather  in  a  condition  of  actual 
equilibrium.  We  shall  continue  to  disregard  the  former  condition 
of  apparent  equilibrium,  due  to  insufficient  reaction  velocity. 

Since  we  have  learned  by  experience  that  existent  differences 
of  temperature  and  pressure  tend  spontaneously  towards  equali- 
zation, we  conclude  that  the  same  temperature  and  the  same  pressure 
prevail  in  every  part  of  a  system  which  is  in  equilibrium.  (Obvi- 
ously, all  effects  of  gravitation,  capillarity,  etc.,  are  excluded 
from  present  consideration.) 

Furthermore,  it  is  at  once  clear  that  an  heterogeneous  system 
cannot  be  in  equilibrium  unless  equilibrium  prevails  in  each  of 


HETEROGENEOUS  EQUILIBRIUM.  27 

the  homogeneous  systems  or  phases  of  which  it  is  composed.  Hence, 
different  parts  of  the  same  phase  cannot  differ  in  composition; 
equalization  would  be  effected  by  diffusion. 

As  a  further  condition  governing  heterogeneous  equilibrium, 
we  now  add  that  the  phases  must  be  in  equilibrium  among  them- 
selves. The  following  general  principle  holds  relative  to  the 
effect  of  the  quantity  of  each  phase  present: 

The  equilibrium  is  independent  of  the  quantity  of  the  phases. 

We  shall  regard  this  as  an  empirical  principle  which  has  thus 
far  stood  every  experimental  test.  (This  principle  is  also  sub- 
stantiated from  a  molecular-theoretical  point  of  view.1)  Some 
of  the  simpler  facts  which  may  be  provisionally  introduced  by 
way  of  confirming  the  above  principle  are  as  follows:  At  the 
temperature  where  1  kilogram  of  ice  and  1  milligram  of  water 
are  capable  of  indefinite  existence  in  the  presence  of  one  another, 
1  kilogram  of  ice  and  1  milligram  of  water  are  also  capable  of 
indefinite  coexistence.  At  the  temperature  where  a  saturated 
solution  fails  to  dissolve  any  portion  of  1  milligram  of  the  sub- 
stance with  which  it  is  saturated,  the  solution  will  be  just  as 
incapable  of  dissolving  more  material  when  1  kilogram  is  open 
to  treatment.  Thus,. the  equilibrium  between  a  crystalline  variety 
and  melt  is  not  altered  when  the  quantity  of  crystalline  material 
is  either  increased  or  decreased.  Hence,  it  follows  that  the 
condition  of  equilibrium  is  uninfluenced  by  the  manner  in  which 
the  crystals  are  distributed  throughout  the  melt  —  whether  in 
the  form  of  one  large  crystal,  or  of  many  small  ones.  Since, 
according  to  the  above  principle,  a  single  crystalline  splinter 
suffices  to  determine  the  condition  of  equilibrium,  no  effect  can 
attend  the  introduction  of  a  further  quantity  of  the  same  crys- 
talline variety,  irrespective  of  the  manner  in  which  the  new 
quantity  is  disposed  throughout  the  liquid.  It  is  then  evident 
that  when  a  system  is  to  be  characterized  by  the  number  of  its 
phases,  each  crystalline  variety  must  be  counted  as  a  single  phase 
only,  however  it  may  be  distributed. 

This  latter  observation  may  be  generalized  in  the  form  of  a 
second  principle: 

The  equilibrium  is  independent  of  the  arrangement  of  the  separate 
phases. 

1  NERNST,  Theoretische  Chemie,  4th  ed.,  1903,  p.  459. 


28 


THE  ELEMENTS  OF  METALLOGRAPHY. 


On  this  basis,  it  is  immaterial  which  of  the  phases  are  in  direct 
contact.  If  two  phases  B  and  C  are  both  in  equilibrium  with 
the  same  third  phase  A,  then  they  are  also  in  equilibrium  with 
one  another.  The  proof  of  this  self-evident  principle  is  simple 
and  is  founded  upon  the  experimental  fact  that  when  two  sub- 
stances which  can  react  with  one  another  are  brought  in  contact, 
such  reaction  finally  ceases.  That  is,  a  condition  of  equilibrium 
occurs  sooner  or  later  in  every  system,  and  when  the  latter  is 
thereafter  protected  from  changes  of  temperature  and  pressure 
a  condition  of  rest  persists.  Now,  our  contention  is  that  when 


B 

A 

O 

FIG.  SA. 

this  condition  of  equilibrium  has  once  resulted  in  a  system  whose 
phases  are  arranged  as  in  Fig.  8a,  it  will  continue  if  the  two  phases 
B  and  C  are  brought  into  direct  contact.  To  prove  this,  let  the 
phases  be  arranged  in  a  ring  as  shown  in  Fig.  8b,  B  and  C  touch- 
ing one  another.  Let  the  ring  be  entirely  closed  and  possessed 
of  rigid  walls,  so'  that  changes  in  atmospheric  pressure  can  have 

no  effect  upon  the  system.  To  guard 
against  temperature  changes,  let  it  be 
immersed  in  a  large  bath  of  some 
liquid  which  may  be  maintained  at 
constant  temperature.  Now,  if  B  and 
C  were  not  in  equilibrium,  they  would 
react  with  one  another  and  sustain 
mutual  alteration.  Then,  as  soon  as 
these  two  phases  had  reached  equi- 
librium with  one  another,  they  would 
no  longer  be  in  equilibrium  with  A. 
On  regaining  equilibrium  with  A,  they 

would  again  cease  to  be  in  equilibrium  with  one  another.  Thus 
it  appears  that  such  a  system  would  never  come  to  rest,  a 
result  entirely  at  variance  with  actual  experience  (impossibility 
of  perpetual  motion  of  the  second  kind).  Hence,  B  and  C  must 
be  in  equilibrium  when  in  contact. 


FIG.  SB. 


HETEROGENEOUS  EQUILIBRIUM.  29 

The  above  argument  implies  a  certain  qualification  to  the  effect  that 
division  of  any  phase  shall  not  be  carried  far  enough  to  bring  the  ques- 
tion of  surface  energy  into  prominence.  As  a  matter  of  fact,  the  solu- 
bility of  a  substance  depends  somewhat  upon  its  state  of  division;  large 
crystals  are  less  soluble  than  small  ones.  It  is  possible  for  such  differ- 
ences in  solubility  to  become  considerable  when  the  fineness  of  division 
exceeds  a  certain  limit.  We  shall  omit  all  consideration  of  such  cases  as 
unimportant  in  the  present  connection. 

The  two  foregoing  principles  are  of  particular  significance  in 
that  they  serve  by  way  of  differentiation  between  the  various 
types  of  heterogeneous  equilibrium  which  we  shall  encounter. 
In  the  above  terms,  a  system  is  completely  characterized  as 
regards  its  state  of  equilibrium  by  the  following  classes  of  data: 

(1)  Data  concerning  the  pressure  under  which  the  system  is 
existent.     This  pressure  must  be  uniform  in  all  parts  of  the 
system,  and  we  shall  invariably  assume  the  same  to  equal  one 
atmosphere  —  regarded  as   mechanical   pressure  operating  upon 
the  system. 

(2)  Data   concerning  the  temperature  of  the  system,   which 
must  also  be  uniform  throughout. 

(3)  Data   concerning   the   number   of   phases   composing   the 
system. 

(4)  Data  concerning  the  composition  of  each  and  every  phase, 
and  its  state  of  aggregation;    where  polymorphism  occurs,  such 
data  to  define  the  modification  in  question. 

Data  relative  to  the  quantity  of  material  represented  by  the 
separate  phases,  as  well  as  to  the  arrangement  of  phases,  is  super- 
fluous in  this  connection. 

The  system  may  undergo  change  in  temperature  or  pressure 
(the  latter  excluded  under  present  conditions)  as  a  result  of  heat 
addition  or  abstraction,  etc.  Again,  new  phases  may  appear, 
or  current  phases  disappear.  Finally,  the  composition  of  one 
or  more  phases  may  change.  If  heat  addition  or  abstraction 
causes  no  change  in  the  number  or  composition  of  at  least  one 
phase,  but  merely  alters  the  quantity  of  material  in  any  of  the 
phases,  the  current  condition  of  equilibrium  remains  unaffected; 
there  is  no  attendant  temperature  change. 

We  shall  proceed  to  elucidate  these  general  relations  by  way 
of  several  simple  examples,  turning  first  of  all  to  the  reversible 


30  THE  ELEMENTS  OF  METALLOGRAPHY. 

process  of  fusion  and  crystallization.  Suppose  that  a  pure  sub- 
stance which  melts  without  decomposition  has  been  heated  to 
such  an  extent  that  a  portion  is  in  the  molten  condition.  If  the 
system  is  now  protected  from  any  flow  of  heat  in  either  direction, 
no  further  change  takes  place;  the  quantity  of  melt  and  of  crys- 
talline material  each  remains  constant  for  an  indefinite  length  of 
time;  the  system  is  in  a  condition  of  equilibrium.  Such  equi- 
librium is  characterized  by  the  pressure  exerted  upon  the  system 
by  the  atmosphere  —  assumed  to  be  invariable  —  by  the  tem- 
perature and  by  the  number  (two)  of  phases.  The  latter  are 
described  by  the  terms  crystalline  and  liquid,  and  both  possess 
the  same  percentage  composition.  If  we  proceed  to  supply  the 
system  with  heat,  transformation  of  a  definite  quantity  of  these 
crystals  into  liquid  results.  Does  an  elevation  of  temperature 
attend  this  change?  Such  is  not  possible  while  the  crystalline 
phase  remains  at  all  represented  in  the  system.  For  we  know 
that  the  condition  of  equilibrium  is  not  qualified  by  the  quantity 
of  material  representing  any  phase  of  the  system.  It  is  merely 
a  decrease  in  the  quantity  of  crystals  and  an  increase  in  the 
quantity  of  melt  which  we  effect  by  heat  addition;  no  change 
in  the  composition  of  either  phase  is  brought  about.  Therefore 
the  temperature  must  remain  constant.  Moreover,  it  cannot 
change  until  the  last  crystalline  splinter  has  melted.  At  this 
point,  the  process  of  fusion  becomes  complete  owing  to  exhaus- 
tion of  one  phase,  and  addition  of  heat  is  thereupon  attended 
by  elevation  of  temperature. 

A  similar  line  of  reasoning  may  be  employed  when  we  are 
dealing  with  abstraction  of  heat  from  the  system.  The  solidi- 
fication process  continues  until  the  last  drop  of  liquid  is  exhausted, 
whereupon  further  heat  abstraction  effects  a  fall  in  temperature. 
Thus  it  appears  that  the  fusion  of  pure  substances  at  definite 
and  invariable  temperature  under  atmospheric  pressure  (where 
no  decomposition  ensues)  and  their  complementary  solidification 
at  the  same  temperature  constitute  a  special  case  under  the 
general  principle  that  the  equilibrium  of  a  heterogeneous  system 
bears  no  relation  to  the  quantity  of  material  appearing  in  each 
of  the  phases  which  make  up  the  system. 

The  occurrence  of  polymorphous  transformation  at  definite 
temperature  also  appears  in  the  same  light. 


HETEROGENEOUS  EQUILIBRIUM.  31 

We  shall  now  take  up  a  special  case  which  will  serve  to  illus- 
trate a  type  of  phenomenon  frequently  observed  in  the  alloy 
field,  for  the  explanation  of  which  we  are  indebted  to  TAMMANN.* 
It  often  happens  that  a  pure  inter-metallic  compound  fails  to 
melt  unchanged,  but  undergoes  partial  liquefaction  only,  when 
heated  to  the  proper  temperature.  At  the  same  time,  a  crys- 
talline variety  of  different  composition  is  separated.  The  reverse 
process  occurs  on  cooling  the  mixture.  Thus,  VoGEL2  observed 
that  a  gold-lead  compound  of  the  formula  Au2Pb  decomposes,  on 
heating,  to  melt  and  a  new  crystalline  variety,  viz.,  pure  gold. 
In  order  to  bring  about  fusion  of  the  gold,  and  thus  obtain  a 
homogeneous  melt,  further  elevation  of  temperature  is  necessary. 
Conversely,  the  first  crystals  which  separate  on  cooling  a  melt 
of  the  composition  Au2Pb  consist  of  pure  gold,  and  these  react 
with  the  remaining  melt  at  some  lower  temperature  to  form  the 
compound  Au2Pb.  The  stoichiometrical  relations  for  this  process 
are  given  in  the  following  equation,  which  at  first  sight  appears 
somewhat  unusual  in  form: 

Au2Pb  <=»  0.722  Au  +  Melt  (1.278  Au  +  1  Pb). 

Verbally,  this  indicates  that  1  gram  molecule  of  the  compound 
Au2Pb  yields  when  heated  0.722  gram  atoms  of  gold  and  a  quan- 
tity of  melt.  The  composition  of  this  melt  in  gram  molecules 
or  gram  atoms,  respectively,  is  of  course  given  by  the  difference 
between  1  gram  molecule  of  the  compound  Au2Pb  and  the  quan- 
tity of  separated  gold,  i.e.,  (2  Au  +  IPb)  -  0.722  Au  =  1.278 
Au  +  1  Pb. 

The  composition  of  this  melt  expressed  in  percentage  form  is 
45  per  cent  Pb  +  55  per  cent  Au. 

The  arrows  indicate  reversibility  of  the  process,  whereby  the 
reaction  may  proceed  towards  the  right  or  left,  according  as 
addition  or  abstraction  of  heat  is  brought  about. 

We  again  raise  the  question  as  to  whether  decomposition  of 
the  pure  compound  and  the  associated  recombination  of  its  dis- 
sociation products  does  or  does  not  proceed  at  constant  tem- 
perature. In  answering  this  question  we  need  only  consider 
what  takes  place  on  cooling  after  the  compound  has  once  been 

1  TAMMANN,  Z.  anorg.  Chem.,  37,  303  (1903). 

2  VOGEL,  Z.  anorg.  Chem.,  45,  11  (1905). 


32  THE  ELEMENTS  OF  METALLOGRAPHY. 

heated  to  the  point  where  partial  decomposition  into  pure  gold 
and  melt  will  have  resulted.  When  heating  has  been  carried 
thus  far,  and  the  system  is  isolated  as  regards  flow  of  heat  in 
either  direction,  we  have  equilibrium  between  the  following 


(1)  A   crystalline  variety   composed  of   the  pure    compound 
Au2Pb, 

(2)  A  crystalline  variety  composed  of  pure  gold, 

(3)  Melt  of  the  composition  1.278  Au  +  1  Pb. 

Our  authority  for  such  assertion  of  equilibrium  lies  in  the 
observation  that  no  change  takes  place  within  the  closed  system. 
Neither  the  quantity  of  crystals  (of  either  variety)  nor  of  melt 
changes,  while  the  temperature  remains  constant  under  constant 
pressure.  Now,  when  the  system  is  supplied  with  an  additional 
quantity  of  heat,  further  decomposition  of  the  compound  Au2Pb 
into  pure  gold  and  melt  ensues.  In  this  way  the  quantity  of 
"Au2Pb"  crystals  decreases,  while  the  quantity  of  "pure  gold" 
crystals  and  that  of  melt  increase.  But,  obviously,  the  melt 
formed  at  first  possesses  the  same  composition  as  that  formed 
subsequently.  The  composition  of  each  and  every  phase  remains 
unchanged;  the  quantity  alone  changes.  Therefore,  there  can 
be  no  change  of  temperature  until  the  last  crystal  of  Au2Pb  has 
decomposed  into  pure  gold  and  melt,  and  it  appears  that  a  com- 
pound which  melts  under  decomposition,  as  above,  is  as  well 
characterized  by  a  constant  point  of  decomposition  and  of  forma- 
tion as  is  a  compound  which  melts  unchanged  by  a  constant 
melting  point  and  freezing  point.  We  shall  not  hesitate  to  apply 
the  more  concise  term,  melting  point,  to  a  temperature  of  decom- 
position, for  obvious  reasons. 

We  may  summarize  previous  developments  as  follows: 

When  in  a  reversible  process  the  quantity  but  not  the  composition 
of  the  separate  phases  sustains  alteration,  owing  to  addition  or 
abstraction  of  heat,  the  temperature  remains  constant,  for  constant 
pressure,  until  some  phase  becomes  completely  exhausted. 

And  conversely: 

When,  on  adding  heat  to  or  abstracting  heat  from  a  system,  it  is 
observed  that  the  temperature  remains  unchanged  under  constant 
pressure,  it  follows  that  the  quantity  but  not  the  composition  or 
number  of  the  separate  phases  has  sustained  alteration. 


HETEROGENEOUS  EQUILIBRIUM.  33 

These  considerations  are  based  upon  the  principle  that  in  any, 
system  the  condition  of  equilibrium  is  unaffected  by  variation 
in  the  quantity  of  any  phase,  or  phases.  Hence,  they  appear 
justifiable  only  in  the  event  that  the  system  remain  continually 
in  the  equilibrium  condition  during  addition  or  abstraction  of  heat. 
In  other  words,  the  process  must  be  not  only  theoretically  revers- 
ible, but  it  must  be  actually  carried  out  reversibly.  Thus,  the 
reaction  velocity  of  the  process  in  question  must  in  every  instance 
be  great  enough  to  exceed  the  rate  of  addition  and  abstraction  of 
heat:  the  process  must  be  regulated  by  the  flow  of  heat  alone. 
When  this  is  not  the  case,  abnormalities,  such  as  supercooling, 
etc.,  will  develop,  and  the  above  principle  become  invalid. 

Adopting  Roozeboom's  phraseology,  we  shall  characterize  that 
form  of  equilibrium  in  heterogeneous  systems,  wherein  change 
in  the  quantity  of  separate  phases,  but  not  in  their  composition, 
is  effected  by  addition  or  abstraction  of  heat  under  constant 
pressure,  as  complete  heterogeneous  equilibrium,  or  in  a  word, 
complete  equilibrium. 

In  contradistinction  to  complete  equilibrium  we  have  incomplete 
(heterogeneous)  equilibrium,  wherein  not  only  the  quantity  of 
separate  phases,  but  the  composition  of  at  least  one  phase  as 
well,  is  altered  during  the  reversible  process  attending  addition 
of  heat  to  or  abstraction  of  heat  from  the  system.  This  type  of 
heterogeneous  equilibrium  is  well  illustrated  by  the  solidification 
of  salt  solutions.  We  are  well  aware  that  water  may  be  frozen 
by  abstraction  of  heat,  and  that  ice  may  be  melted  by  addition 
of  heat.  The  process  is  therefore  reversible,  and  may  be  repre- 
sented by  the  expression 

H20solid  <=^  H20iiquid, 

in  which  the  arrows  indicate  reversibility,  as  on  the  previous 
occasion.  When  pure  liquid  water  and  ice  are  in  equilibrium, 
addition  of  heat  to  or  abstraction  of  heat  from  the  system  causes 
change  in  the  quantity  of  each  phase,  but  no  change  in  its 
composition:  the  process  takes  place  at  constant  temperature 
(at  0  degrees)  under  constant  pressure,  and  we  are  dealing  with 
complete  equilibrium. 

If  we  dissolve  a  second  substance,  e.g.,  common  salt,  in  pure 
water  and  abstract  heat  from  the  solution,  it  is  found  that  pure 
ice  separates,  at  least  from  solutions  which  are  not  too  concen- 


34  THE  ELEMENTS  OF  METALLOGRAPHY. 

trated.  Thus,  we  now  have  pure  ice  in  equilibrium  with  a  solu- 
tion of  common  salt.  Obviously,  the  equilibrium  temperature 
of  this  system  need  not  be  the  same  as  that  of  the  former  system 
(ice-water),  and,  indeed,  we  know  that  it  is  not  the  same. 
If  we  continue  to  abstract  heat  from  the  system,  the  quantity 
of  ice  increases  and  the  quantity  of  liquid  decreases.  Since, 
however,  a  single  constituent  is  removed  from  the  liquid  phase, 
namely,  pure  water,  this  phase  becomes  richer  in  its  other  con- 
stituent, namely,  common  salt.  Hence,  one  phase  changes  in 
composition  during  this  process,  i.e.,  we  are  dealing  with  incom- 
plete equilibrium.  The  temperature  must  change  as  ice  freezes 
out,  and  experience  shows  that  the  temperature  of  a  freezing 
salt  solution  falls  continuously  (down  to  a  certain  point).  If, 
contrary  to  the  actual  state  of  affairs,  the  composition  of  this 
solid  phase  were  identical  with  that  of  the  solution,  we  should 
look  for  no  change  in  temperature  during  solidification. 

Apart  from  the  above  classification  of  systems  into  such  as 
show  complete  or  incomplete  equilibrium,  we  are  called  upon  to 
consider  another  type  of  distinction  between  systems  which  are 
in  heterogeneous  equilibrium:  one  which  is  generally  brought 
into  requisition,  and  which  will  be  used  extensively  in  this  text. 
We  refer  to  classification  according  to  the  number  of  indepen- 
dently variable  constituents  or,  briefly,  components  of  the  system. 
We  have  on  this  basis,  one  component  systems,  two  component 
or  binary  systems,  three  component  or  ternary  systems,  etc. 
In  the  case  of  metallic  alloys,  the  number  of  independent  con- 
stituents is  equal  to  the  number  of  metals  present,  at  any  rate 
as  far  as  the  investigation  deals  with  all  possible  combinations 
of  the  respective  metals  with  one  another. 

Accurately  speaking,  a  system  possesses  as  many  independent  con- 
stituents, or  components,  as  the  number  of  different  substances  which 
are  necessary,  and  will  suffice,  for  construction  of  each  and  every  phase  in 
question.  Consequently,  this  number  cannot  be  given  until  the  compo- 
sition of  each  and  every  phase  of  the  system  under  investigation  is  known. 
Moreover,  it  depends  upon  the  precise  nature  of  change  considered  in 
the  system,  and  hence  may  not  be  placed  unqualifiedly  equal  to  the  num- 
ber of  elements  which  appear  in  the  system.  A  few  examples  will  serve 
to  make  this  clear.  We  are  well  aware  that  ice  does  not  change  in  per- 
centage composition  on  transformation  into  the  liquid  state.  The  infor- 


HETEROGENEOUS  EQUILIBRIUM.  35 

mation  that  ice  contains  a  grams  H2O  and  liquid  water,  b  grams  H2O 
per  cubic  centimeter  is,  therefore,  ample  for  the  purpose  of  defining  the 
composition  of  each  and  every  phase  in  the  system,  Ice-Liquid  water. 
Hence,  this  must  be  regarded  as  a  one  competent  system  under  the 
present  specification.  The  same  is  obviously  true  in  relation  to  any 
pure  substance  melting  without  decomposition,  provided  we  confine  our 
investigation  to  the  configuration,  Crystalline-Melt. 

If,  however,  a  substance  which  melts  under  decomposition  is  investi- 
gated—  the  compound  Au2Pb  (discussed  on  p.  31),  for  example  —  it  is 
found  that  the  composition  of  the  different  phases  cannot  be  defined  in 
terms  of  Au2Pb  (a,  b  or  c  grams  of  the  compound  per  cubic  centimeter). 
For,  one  of  the  phases  derived  from  the  compound  is  lead-free,  as  we  have 
seen  (pure  gold),  and  the  other,  viz.,  melt,  consists  of  gold  and  lead  in 
some  proportion  other  than  that  which  corresponds  to  the  above  formula. 
Accordingly,  two  substances  must  be  used  (and  only  two  need  be  used) 
in  defining  the  percentage  composition  of  each  and  every  phase.  Hence, 
we  regard  this  as  a  two  component  system.  The  choice  of  components 
is  left  more  or  less  to  our  discretion.  We  choose  gold  as  one,  since  one 
phase  is  composed  of  pure  gold.  When  lead  is  chosen  as  the  other,  the 
atomistic  composition  of  the  three  phases  becomes,  Au,  2  Au  + 1  Pb,  and 
1.278  Au  +  1  Pb,  as  explained  on  p.  31.  But  when  the  gold  lead  com- 
pound AuPba1  is  chosen  as  the  second  independent  constituent,  the  com- 
position of  the  three  phases  must  be  expressed  as  follows : 

(1)  The  crystalline  variety  pure  gold  by  Au, 

(2)  The  crystalline  variety  Au2Pb  by  AuPb2  +  3  Au, 

(3)  The  melt  1.278  Au  +  1  Pb  by  AuPb2  +  1.556  Au. 

Either  assumption  is  permissible,  inasmuch  as  it  is  actually  possible  to 
build  up  the  particular  system  by  using  the  substances  herein  chosen  as 
components.  Hence  it  follows  that  in  classifying  systems  we  are  free  to 
use  the  number  of  independent  constituents,  but  are  not  justified  in  impos- 
ing any  specification  as  to  their  nature,  viz.,  whether  elements  or  com- 
pounds; this  is  more  or  less  optional. 

Suppose  that  the  compound  Au2Pb  were  to  undergo  polymorphous 
transformation  at  some  point  below  its  decomposition  temperature. 
Then,  in  studying  the  equilibrium  between  these  two  crystalline  varieties 
of  the  same  composition  we  should  be  dealing  with  a  one  component 
system  in  which  Au2Pb  is  the  component. 

Turning  to  a  system  produced  by  fusion  of  mixed  PbO  and  PbCl22,  we 
note  the  following:  As  long  as  the  correct  proportions  of  lead,  oxygen, 
and  chlorine  in  each  and  every  phase  may  be  given  in  the  form,  a  grams 
PbO  +  b  grams  PbCl2  per  cubic  centimeter,  the  system  is  to  be  regarded 

1  VOGEL,  1.  c.,  p.  31.  2  RUER,  Z.  anorg.  Chem.,  49,  365  (1906). 


36  THE  ELEMENTS  OF  METALLOGRAPHY. 

as  constructed  from  two  independent  constituents.  When  our  investi- 
gation is  restricted  to  the  fusion  and  solidification  process  associated  with 
the  compound  PbCl2  +  2  PbO  (at  693  degrees),  we  are  dealing  with  a  one 
component  system,  although  three  elements  are  concerned  in  the  change. 
If,  however,  the  compound  PbCl2  should  undergo  decomposition  during 
any  alteration  in  the  system  —  whereby  it  would  be  necessary  to  indicate 
the  composition  of  one  phase  after  the  manner,  a  PbO  +  6  PbCl,  and  that 
of  the  other  after  the  manner,  c  PbO  +  d  PbCl3  —  we  should  be  obliged 
to  regard  the  system  as  embracing  three  components  with  respect  to  this 
particular  change. 

A  system  embracing  hydrogen,  oxygen  and  water  at  ordinary  temper- 
ature, where  no  appreciable  combination  of  hydrogen  and  oxygen  occurs, 
must  be  regarded  as  a  three  component  system,  notwithstanding  the  fact 
that  only  two  elements  are  present.  At  some  higher  temperature,  where 
the  above  combination  is  sufficiently  rapid,  the  two  elements  alone  would 
appear  as  components.  The  same  effect  might  be  secured  through  the 
action  of  a  catalysing  agent,  platinum  sponge,  for  example.  However, 
all  cases  of  this  sort  do  not  properly  belong  here,  since  we  have  made  an 
assumption  of  actual  equilibrium  in  every  phase  to  the  exclusion  of  all 
apparent  equilibria. 

The  conception  of  independent  constituents  of  a  phase  system  plays  an 
important  role  in  the  doctrine  of  heterogeneous  equilibrium,  owing  to  the 
fact  that  an  exceedingly  simple  relation  exists  between  the  number  of 
phases  which  are  in  complete  heterogeneous  equilibrium  and  the  num- 
ber of  independent  constituents  of  the  system.  This  was  developed  by 
WILLARD  GIBBS  x  and  forms  what  is  known  as  the  phase  rule.  (Cf. 
remarks  upon  this  subject  supplementing  Chapter  IV.)  We  shall,  how- 
ever, make  little  use  of  this  rule  in  our  general  presentation  of  the 
subject. 

In  this  chapter,  we  have  dealt  with  those  transformations  which 
a  pure  substance  undergoes  without  changing  its  composition,  and 
have,  therefore,  made  the  chapter  heading,  ONE  COMPONENT 
SYSTEMS.  As  is  well  known,  metallic  alloys  are  prepared  by 
fusing  two  or  more  metals  together,  whence  our  attention  is  trans- 
ferred to  Two  COMPONENT  SYSTEMS  as  a  subject  for  the  next 
chapter,  and  to  THREE  COMPONENT  SYSTEMS  for  subsequent  treat- 
ment. The  investigations  of  the  last  few  years  have,  nevertheless, 
been  almost  exclusively  confined  to  two  component  systems. 
There  have  been  very  few  systematic  investigations  dealing  with 
ternary  alloys,  and  none  at  all  dealing  with  quaternary  alloys. 

1  loc.  cit.,  p.  25. 


CHAPTER  III. 
TWO  COMPONENT  SYSTEMS. 

MUTUAL  SOLUBILITY  AND  STATE  OF  AGGREGATION. 

THE  susceptibility  of  two  substances  to  mutual  mixture  is 
dependent  to  a  marked  degree  on  their  state  of  aggregation. 

It  is  well  known  that  gases  are  miscible  with  one  another  in 
all  proportions.  We  must  differentiate  between  two  cases  of 
miscibility  in  the  liquid  state;  two  liquids  are  either  completely 
miscible  with  one  another,  as  are  alcohol  and  water  and  the 
greater  number  of  molten  metals,  or  they  are  miscible  with  one 
another  (dissolve  one  another)  to  a  limited  extent  only.  In  the 
latter  case,  the  two  liquids,  owing  to  their  difference  in  density, 
become  separated  from  one  another  and  appear  in  two  layers 
after  standing  for  a  time.  When  the  liquids  are  in  a  condition 
of  equilibrium,  each  has  of  course  dissolved  the  other  to  the  point 
of  saturation.  The  saturation  concentration  varies  to  an  excep- 
tional degree  with  different  liquids,  and  is,  moreover,  highly  de- 
pendent on  the  temperature.  Water-ether  and,  of  the  metals 
(which  may  be  characterized  as  comparatively  prominent  in 
showing  this  condition),  lead-zinc,  may  serve  as  examples  of 
limited  solubility  in  one  another.  The  extraction  of  silver  from 
lead  by  the  Parkes  Process  is  founded  upon  the  latter  case  of 
limited  miscibility. 

The  capability  of  substances  to  mix  with  one  another  is  further 
reduced  in  the  crystalline  state.  Nevertheless,  many  pairs,  etc., 
of  substances  which  mutually  dissolve  in  the  crystalline  condition 
in  all  proportions,  or  which,  as  is  commonly  said,  form  complete 
series  of  mixed  crystals,  are  known.  By  way  of  example,  we  may 
cite  silver-gold.  Limited  miscibility  in  the  crystalline  state  is 
illustrated  by  the  gold-nickel  series.  On  account  of  the  generally 
limited  miscibility  of  substances  when  in  the  crystalline  state,  we 
frequently  observe  that  a  mixture  which  is  homogeneous  in  the 
liquid  state,  separates  on  crystallization.  Investigation  of  crystals 

37 


38  THE  ELEMENTS  OF  METALLOGRAPHY. 

which  have  been  removed  from  a  partially  solidified  mixture  and 
freed  from  adherent  mother  liquor  frequently  shows  that  these 
represent  one  component  alone,  or  at  any  rate  a  practically  pure 
component.  Crystallization  from  aqueous  and  other  solutions, 
which  are  so  commonly  carried  out  in  the  chemical  laboratory, 
afford  excellent  illustration  of  such  immiscibility  in  the  crystalline 
condition.  The  gold-thallium  series  will  serve  in  this  connection 
as  an  example  taken  from  the  alloy  field.  Thus,  from  a  purely 
practical  standpoint  we  are  in  a  position  to  speak  of  immiscibility 
in  the  crystalline  state,  although  this  case  must  be  theoretically 
regarded  as  an  extreme  condition  of  limited  miscibility. 

The  varying  degree  of  miscibility  in  the  liquid  and  crystalline 
states  serves  in  connection  with  the  possible  existence  or  non- 
existence  of  chemical  compounds  as  a  criterion  for  the  classifica- 
tion of  two  component  systems. 

§  1.  THE  Li  QUID  STATE  is  CHARACTERIZED  BY  COMPLETE  MISCIBIL- 
ITY; THE  CRYSTALLINE  STATE  BY  COMPLETE  IMMISCIBILITY. 

The  following  statement  summarizing  a  general  result  of  prac- 
tical experience  will  be  adopted  as  a  broad  basis  for  subsequent 
developments: 

When  two  pure  substances  are  miscible  in  the  liquid  state  and 
immiscible  in  the  crystalline  state,  the  temperature  of  solidification 
of  each  substance  will  be  lowered  by  addition  of  the  other. 

This  generalization  is  commonly  known  as  the  LAW  OF  FREEZING 
POINT  OR  MELTING  POINT  LOWERING.  By  the  term,  tempera- 
ture of  solidification,  is  meant  the  temperature  at  which  crystalli- 
zation begins. 

As  we  have  seen  above,  this  preassumed  immiscibility  in  the 
crystalline  state  implies  that  each  of  the  two  substances  separates 
from  the  melt  in  the  pure  condition.  If  such  is  not  the  case,  the 
law  of  freezing  point  lowering  loses  its  validity. 

A.   Polymorphous    Transformations   do   not   Occur.     The   Compo- 
nents do  not  Unite  to  Form  a  Chemical  Compound. 

I.  THE  CRYSTALLIZATION  OF  AQUEOUS  SOLUTIONS  OF  COMMON 
SALT.  —  We  will  again  take  up  the  subject  of  crystallization  of  an 
aqueous  solution  of  common  salt,  with  due  regard  to  the  law  of 


TWO  COMPONENT  SYSTEMS.  39 

freezing  point  lowering  and  to  the  views  which  we  have  acquired 
through  previous  consideration  of  heterogeneous  equilibrium.1 
A  solution  of  this  sort  represents  a  two  component  system  in 
which  the  components  are  water  and  salt,  and  the  fact  that 
water,  in  the  form  of  pure  ice,  separates  first  of  all  on  cooling 
the  dilute  solution,  while  salt,  likewise  in  the  pure  condition, 
first  separates  on  cooling  a  concentrated  salt  solution  (for  example, 
a  solution  which  is  saturated  at  100  degrees),  certifies  that  our 
required  condition  of  immiscibility  in  the  crystalline  state  actually 
obtains.  Pursuant  to  general  usage  covering  such  cases,  we  shall 
designate  water  as  the  solvent  and  common  salt  as  the  dissolved 
substance. 

We  will  now  assume  that  a  dilute  salt  solution,  containing 
some  two  and  a  half  per  cent  of  salt,  is  allowed  to  freeze  com- 
pletely, during  which  process  continual  observation  of  tempera- 
ture is  made.  Owing  to  the  freezing  point  lowering  of  water 
following  the  addition  of  salt,  no  freezing  occurs  at  0  degrees,  the 
true  freezing  point  of  pure  water.  Separation  of  ice  crystals  is 
first  observed  at  about  —1.5  degrees.  By  reason  of  this  separa- 
tion of  ice,  the  residual  solution  becomes  richer  in  common  salt;  a 
condition  of  incomplete  equilibrium  is  then  at  hand  and  we  shall 
not  expect  complete  solidification  of  the  solution  to  occur  at  the 
above  temperature,  —1.5  degrees.  If,  then,  complete  solidifica- 
tion does  not  occur  at  —1.5  degrees,  as  is  actually  the  case,  it  is 
self-evident  that  the  freezing  point  of  the  enriched  salt  solution 
lies  at  a  lower  temperature;  it  could  not  lie  higher,  for  then  the 
solution  would  not  be  in  equilibrium  at  —1.5  degrees,  but  would 
be  existent  below  its  true  freezing  point,  or,  in  other  words,  it 
would  be  supercooled  and  therefore  in  a  labile  condition.  We 
may,  thus,  make  the  general  statement: 

//  a  solution  does  not  crystallize  at  constant  temperature,  its 
freezing  point  must  fall  as  freezing  progresses. 

To  secure  further  separation  of  ice,  we  must,  then,  cause  the 
temperature  to  fall,  i.e.,  the  freezing  point  of  the  salt  solution 
falls,  in  proportion  as  the  latter  becomes  more  concentrated. 
When  half  of  the  water  has  frozen  to  ice,  the  remaining  salt  solu- 

1  Complications  due  to  separation  of  the  hydrate  NaCl-2H2O  (Landolt  & 
Bornstein;  Phys.  Chem.  Tables,  3d  ed.  p.  556)  will  not  be  taken  into  account 
during  this  discussion. 


40  THE  ELEMENTS  OF  METALLOGRAPHY. 

tion  contains  5  per  cent  salt,  and  we  observe  a  freezing  tempera- 
ture of  —3.1  degrees.  When  the  solution  has  attained  a  salt 
content  of  10  per  cent,  or  15  per  cent,  respectively,  its  freezing 
point  will  have  fallen  to  —6.7  degrees,  or  —12.2  degrees. 

Now,  an  unlimited  depression  of  the  freezing  point  of  the  salt 
solution  is  not  possible  —  first  of  all  we  need  consider  none  other 
than  purely  experimental  evidence  in  reaching  this  conclusion.  A 
solution  of  minimum  freezing  point  will  accordingly  result  sooner 
or  later,  and  such  a  solution  must  obviously  freeze  completely  at 
this  temperature,  for  the  very  reason  that  it  can  have  no  lower 
freezing  temperature.  For  an  aqueous  solution  of  common  salt 
this  temperature  is  —22.4  degrees.  Thus,  we  observe,  on  allow- 
ing the  freezing  process  to  continue  progressively,  that  the  tem- 
perature sinks  continuously  until  —22.4  degrees  is  reached, 
when  further  abstraction  of  heat  is  not  attended  by  temperature 
fall  for  the  time  being.  The  thermometer  indicates  this  very 
temperature  until  the  last  residue  of  liquid  has  become  trans- 
formed into  crystalline  material.  Not  until  then  does  the 
temperature  fall  below  this  point.  It  thereupon  proceeds  to 
converge  towards  the  temperature  of  the  surroundings. 

We  learn  by  analysis  of  the  solution  which  solidifies  at  —22.4 
degrees  that  it  contains  23  per  cent  of  common  salt  and  77  per 
cent  of  water.  A  solution  of  this  concentration  solidifies  at  con- 
stant temperature,  after  the  manner  of  a  pure  substance.  But 
such  a  period  of  constant  temperature  during  abstraction  of  heat 
from  the  system  is  our  criterion  for  the  existence  of  complete 
heterogeneous  equilibrium.  In  effect,  throughout  this  period  the 
composition  and  the  number  of  phases  can  sustain  no  alteration. 
That  is  to  say,  the  frozen  material  must  possess  the  same  compo- 
sition as  the  solution.  This  conclusion  is  apparently  substantiated 
by  experiment,  for,  when  a  partially  frozen  aqueous  solution  of 
common  salt  is  viewed  under  the  microscope,  two  different 
crystalline  varieties,  viz.,  ice  crystals  and  common  salt  crystals, 
may  be  plainly  recognized. 

The  mechanism  of  the  process  is  clear  in  the  light  of  the  above 
observation.  Further  concentration  of  the  solidifying  23  per  cent 
salt  solution  is  prevented  in  that  not  only  ice  crystals  but  salt 
crystals  as  well  separate  from  it  on  continued  abstraction  of  heat. 
Moreover,  these  two  crystalline  varieties  separate  from  the  solu- 


a        a 


-20 


-40° 


5  10  «  15  20  25 

Weight  per  cent  Common  Salt 

.  9b.     Fusion  Diagram  of  the  System  Water-Common  Salt.         (41) 


42  THE  ELEMENTS  OF  METALLOGRAPHY. 

tion  in  the  exact  proportion  which  is  descriptive  of  their  presence 
in  the  liquid  state.  From  the  moment  when  the  first  salt  crystals 
appear  in  the  presence  of  ice  crystals,  heat  abstraction  effects  no 
change  in  the  composition  of  either  crystalline  variety,  but  only 
an  increase  in  the  amount  of  both  kinds  of  crystalline  material. 
Until  the  last  drop  of  solution  has  solidified  to  a  mixture  of  salt 
and  ice  crystals,  we  have  complete  equilibrium  and  therefore  con- 
stant temperature.  Then  only  is  it  possible  for  further  abstraction 
of  heat  to  cause  a  fall  in  temperature. 

A  23  per  cent  solution  of  common  salt  in  water  is  thus  charac- 
terized by  a  constant  temperature  of  crystallization  and  fusion,  as 
is  a  pure  substance.  A  mixture  which  crystallizes  and  fuses  as 
above  at  a  minimum  temperature  is  called  an  eutectic  mixture,  or, 
simply  an  eutectic.  For  a  long  time,  such  solutions  and  mixtures 
were  regarded  as  chemical  compounds  owing  to  their  constant 
melting  points  —  notwithstanding  the  difficulty  which  is  experi- 
enced in  representing  their  composition  by  formulas  in  proper 
correspondence  with  the  law  of  multiple  proportions.  It  is  a 
noteworthy  fact  that  GUTHRIE/  who  proposed  the  term  eutectic 
mixture,  and  to  whom  we  are  indebted  for  the  explanation  of 
these  conditions  (particularly  for  our  perception  of  the  general 
conformity  in  behavior  of  solutions  and  alloys  in  this  connection), 
maintained  in  his  first  paper  dealing  with  aqueous  solutions  that 
those  substances  which  melt  at  constant  (minimum)  temperature 
were  chemical  compounds,  and  named  them  cryohydrates.  This 
too,  in  spite  of  the  fact  that  he  correctly  interpreted  the  mechan- 
ism of  the  process  in  all  of  its  details.  The  term  cryohydrate  is 
applied  now  and  then  at  the  present  time  to  such  eutectica  as 
consist  in  part  of  water. 

We  will  proceed  to  further  elucidate  the  process  of  cooling  for 
water  and  variously  concentrated  aqueous  solutions  of  common 
salt  by  making  use  of  cooling  curves  —  it  being  assumed  that 
the  cooling  converges  towards  a  temperature  of  —100  degrees. 
We  will  at  the  outset  suppose  that  the  quantity  of  solution  taken 
for  every  experiment  is  identical,  e.g.,  100  grams;  that  all  solu- 
tions are  heated  to  100  degrees  before  the  actual  registry  of 
experimental  data;  and  that  cooling  progresses  in  every  case 
under  the  same  conditions.  The  curve  marked  0  per  cent  NaCl 
1  GUTHRIE,  Phil.  Mag.,  v,  17,  462  (1884). 


TWO  COMPONENT  SYSTEMS.  43 

in  Fig.  9a  (p.  41)  represents  the  cooling  of  pure  water  whose 
freezing  point  lies  at  0  degrees  C.  Such  values  may  be  con- 
veniently assigned  to  the  time  units,  which  are  entered  upon 
the  abscissa  axis,  as  will  bring  the  period  of  constant  tempera- 
ture for  pure  water,  represented  by  the  portion  be,  up  to  10 
minutes.  The  scale  of  temperatures  along  the  axis  of  ordinates 
is  shown  in  the  figure.  The  above  mentioned  cooling  curve  is 
made  up  of  the  three  parts  ab,  be,  and  cd,  of  which  ab  corre- 
sponds to  the  cooling  of  liquid  water,  be  (halting  point)  to  crystal- 
lization, and  cd  to  the  cooling  of  ice  towards  the  temperature  of 
convergence. 

The  curve  marked  %\  'per  cent  NaCl  (Fig.  9a)  represents  the 
cooling  of  a  2£  per  cent  solution  of  common  salt  in  water  — 
which  process  has  been  described  previously  at  some  length.  Ice 
crystals  first  separate  at  the  point  b,  corresponding  to  —  1.5°C. 
Owing  to  the  heat  liberated  during  crystallization,  a  decrease  in 
the  rate  of  cooling  begins  at  this  point,  which  condition  is  shown 
on  the  cooling  curve  by  a  break  at  b.  At  first,  as  ice  begins  to 
separate,  the  temperature  sinks  very  slowly  —  when  the  sub- 
stance has  become  half  crystallized,  i.e.,  when  the  residual  liquid 
has  become  a  5  per  cent  solution  (NaCl  in  H2O),  the  temperature 
has  fallen  only  1.6  degrees,  having  reached  the  value  — 3.1°C. 
Since  the  amount  of  solution  (yielding  heat  on  crystallization) 
continually  becomes  less,  the  fall  in  temperature  along  the  branch 
be  of  the  curve  becomes  more  rapid  with  lapse  of  time.  When 
the  temperature  has  fallen  to  —22.4°  C,  its  value  at  the  point  c, 
the  solution  contains  23  per  cent  of  common  salt,  and  a  period  of 
constant  temperature,  given  by  the  branch  cd,  and  corresponding 
to  crystallization  of  the  eutectic,  ensues.  This  halting  point 
must  be  of  comparatively  short  duration,  for  the  2£  grams  of 
common  salt  which  were  present  in  our  original  solution  suffice  to 
form  10.87  grams  only  of  23  per  cent  salt  solution.  After  the 
last  residue  of  solution  has  crystallized,  normal  cooling  ensues 
along  the  branch  de,  the  temperature  converging  towards  —100 
degrees.  To  summarize,  then,  the  cooling  curve  of  our  solution 
consists  of  the  four  branches  ab,  be,  cd  and  de. 

The  cooling  curve  of  a  5  per  cent  solution  presents  a  similar 
appearance  .(see  the  curve  marked  5  'per  cent  NaCl  in  Fig.  9a). 
However,  separation  of  ice  commences  here  at  the  somewhat 


44  THE  ELEMENTS  OF  METALLOGRAPHY. 

lower  point  b  (=  —3.1  degrees).  When  half  the  substance  has 
crystallized,  the  solution  contains  10  per  cent  common  salt,  and 
the  temperature  has  reached  —6.7  degrees;  it  has  fallen  3.6 
degrees.  Notwithstanding  the  fact  that  the  freezing  point  low- 
ering is  very  closely  proportional  to  the  salt  content  of  the 
solution  up  to  a  content  of  10  per  cent,  the  fall  in  temperature 
along  be,  which  accompanies  crystallization  of  ice,  is  more  rapid 
from  the  start  in  concentrated  solutions  than  it  is  in  dilute  solu- 
tions. This  is  obviously  due  to  the  far  greater  percentage  change 
in  salt  content  sustained  by  a  concentrated  solution  than  by  a 
dilute  solution,  when  equal  amounts  of  ice  are  frozen  out.  The 
temperature  falls  at  a  continually  increasing  rate  until  the  point 
c  is  reached,  when  the  period  of  eutectic  crystallization  at  —22.4 
degrees  (along  cd)  ensues.  This  period  will  be  exactly  twice  as 
long  as  was  the  case  in  the  2£  per  cent  solution,  for  obviously 
the  5  grams  of  common  salt  present  in  100  grams  of  the  solution 
with  which  we  are  now  dealing  furnish  twice  the  quantity  of 
23  per  cent  salt  solution  as  did  the  2|  grams  of  salt  present  in 
former  solution,  and  consequently,  twice  the  quantity  of  heat  at 
the  halting  point.  After  the  period  of  eutectic  crystallization  has 
transpired,  i.e.,  after  all  the  material  has  crystallized,  the  tem- 
perature falls  normally  as  shown  by  the  branch  de. 

There  is  no  fundamental  difference  between  the  cooling  curves 
of  10  and  15  per  cent  salt  solutions,  respectively  (Fig.  9a),  and 
those  just  considered.  They  also  consist  of  four  branches;  ab, 
which  represents  cooling  of  the  liquid  mixture;  be,  the  branch  of 
retarded  fall  in  temperature  along  which  separation  of  ice  occurs, 
i.e.,  the  branch  which,  as  was  previously  shown,  represents  incom- 
plete equilibrium  between  ice  and  solution  of  progressively 
increasing  concentration;  cd,  a  horizontal  branch  representing  the 
eutectic  halting  point,  along  which  ice  and  crystals  of  common 
salt  are  in  complete  equilibrium  with  solution  of  continually 
decreasing  quantity  but  invariable  composition;  and  finally  de, 
along  which  the  completely  solidified  mixture  cools  convergently 
towards  —100  degrees.  We  note,  however,  that  the  first  sepa- 
ration of  ice  occurs  at  successively  lower  temperatures  in  the 
several  mixtures,  viewed  in  the  order  of  increasing  concentra- 
tion. (The  order  of  their  presentation  and  discussion.)  For  the 
10  and  15  per  cent  solutions  these  temperatures  are  —6.7  degrees 


TWO  COMPONENT  SYSTEMS.  45 

and  —12.2  degrees,  respectively.  Furthermore,  it  is  evident  that 
the  branch  be  joins  the  branch  ab  at  a  wider  angle  (approaching 
180  degrees)  as  we  pass  from  concentration  to  concentration 
(whereby  the  break  b  becomes  more  and  more  indistinct),  and 
that  the  period  of  crystallization  at  the  eutectic  halting  point, 
which  occurs  at  the  same  temperature  in  all  cases,  increases  in 
proportion  to  the  original  salt  content  of  the  solution;  in  the  10 
per  cent  concentration  it  is  four  times,  and  in  the  15  per  cent 
solution  six  times  as  long  as  in  the  2^  per  cent  concentration. 

If  a  solution  possesses  the  same  salt  content  as  the  eutectic 
mixture,  the  break  b  is  of  course  lacking  on  its  cooling  curve.  In 
such  a  case,  when  the  temperature  of  eutectic  crystallization  has 
been  attained,  ice  and  salt  crystals  separate  simultaneously  in 
the  exact  proportions  which  defined  their  previous  existence  in 
the  solution,  but  at  no  time  does  there  occur  any  individual 
crystallization  of  either  component.  During  the  whole  crystalli- 
zation process,  the  temperature  remains  constant,  thereafter  fall- 
ing in  the  regular  manner  towards  its  lower  limit.  The  cooling 
curve  of  a  23  per  cent  aqueous  solution  of  common  salt  (Fig.  9a) 
consists,  then,  of  three  branches,  as  does  that  of  a  pure  substance; 
ac,  which  corresponds  to  cooling  of  the  liquid;  cd,  a  halting  point, 
which  corresponds  to  eutectic  crystallization  at  —22.4  degrees; 
and  de,  which  corresponds  to  cooling  of  the  completely  solidified 
mixture.  The  period  of  eutectic  crystallization  amounts  in  this 
case  to  9.2  times  that  observed  in  a  2|  per  cent  solution,  as  fol- 
lows from  a  simple  calculation:  it  has  attained  its  maximum 
value  here,  since  the  whole  of  the  original  mixture  crystallizes  at 
this  temperature. 

The  23  per  cent  solution  is  the  only  one  which  can  exist  at 
—  22.4  degrees  (provided  we  confine  ourselves,  as  is  continually 
presumed,  to  discussion  of  equilibrium  conditions,  and  abandon 
all  consideration  of  supercooling).  Here,  we  have  complete  equi- 
librium between  ice,  solid  salt  and  a  23  per  cent  solution,  as  has 
been  repeatedly  noted,  and  an  increase  in  the  amount  of  ice  or 
salt  can  have  no  effect  on  the  condition  of  equilibrium,  i.e.,  on  the 
composition  of  the  solution.  This  particular  solution  may  be 
regarded  as  a  saturated  solution  of  salt  at  this  temperature, 
owing  to  the  participation  of  solid  salt  in  the  equilibrium.  Since, 
then,  the  salt  content  of  a  solution,  saturated  at  —22.4  degrees, 


46  THE  ELEMENTS  OF  METALLOGRAPHY. 

amounts  to  23  per  cent,  that  of  any  solution  which  had  originally 
been  more  concentrated  must  have  fallen  to  23  per  cent,  on 
cooling  to  —22.4  degrees.  Therefore,  such  a  solution  must 
become  less  concentrated  as  freezing  progresses,  exactly  the 
reverse  of  the  cooling  effect  on  previously  considered  solutions. 
This  general  conclusion  is  confirmed  by  the  experimental  results. 
The  first  separation  of  crystals  is  indicated  on  the  cooling  curve  of 
a  26.25  per  cent  aqueous  solution  of  common  salt  (Fig.  9a)  by  the 
first  appearance  of  a  period  of  retarded  fall  in  temperature  and 
the  attendant  break  (which  is  none  too  well  marked,  and  has 
therefore  been  exaggerated  in  the  figure)  at  6  (=0°C.).  The 
crystalline  variety  which  separates  along  be  is  not  ice,  however, 
but  pure  salt.  Separation  of  crystals  continues  until  the  tem- 
perature has  fallen  to  —22.4  degrees;  the  salt  content  to  23 
per  cent.  Then  eutectic  crystallization  sets  in  along  the  hori- 
zontal cd,  and  continues  throughout  a  period  which  is  some  4  per 
cent  shorter  than  that  corresponding  to  the  23  per  cent  solution, 
on  account  of  the  proportionately  lesser  amount  of  eutectic  fur- 
nished by  the  solution  in  hand.  After  completion  of  the  eutectic 
crystallization,  a  normal  fall  in  temperature  along  the  branch  de 
ensues.  On  further  increase  in  the  salt  content  of  the  mixtures, 
the  temperature  of  initial  crystallization  rises  rapidly,  in  cor- 
respondence with  the  well-known  fact  that  the  solubility  of  com- 
mon salt  in  water  changes  only  slightly  with  the  temperature. 
For  example,  the  first  separation  of  crystals  from  a  28.1  per  cent 
solution  occurs  at  the  comparatively  high  temperature  of  100 
degrees,  while  the  quantity  of  eutectic  mixture  which  is  left  to 
solidify  at  —22.4  degrees  is  93  per  cent  of  the  whole  original 
mixture. 

It  is  evident  from  the  above  example  that,  in  a  strict  sense,  we 
are  not  entitled  to  follow  general  usage  and  certify  to  a  difference 
between  the  two  components  of  our  system  by  invariably  calling 
one  solvent  and  the  other  dissolved  substance.  On  consideration 
of  a  sufficient  number  of  different  concentrations,  we  cannot  fail 
to  observe  that  both  substances  behave  in  an  analogous  manner. 
When  the  salt  content  is  less  than  23  per  cent,  the  component, 
water,  separates  first  in  the  form  of  crystals;  when  it  is  more 
than  23  per  cent,  the  other  component,  salt,  separates  first. 

In  Fig.  9a,   cooling  curves  of  the  separate  solutions  are  so 


TWO  COMPONENT  SYSTEMS.  47 

arranged  that  the  distances  of  their  respective  6  points  (first 
break  in  the  curves)  from  the  point  c  on  the  curve  for  pure  water 
(first  curve  at  the  left)  are  proportional  to  the  initial  salt  con- 
tents of  the  original  solutions.  If  we  now  pass  a  (dotted)  curve 
through  all  of  these  points,  we  shall  be  in  a  position  to  locate 
the  temperatures  of  initial  crystallization  for  concentrations 
which  have  not  been  investigated  directly.  We  see  at  once  from 
the  figure  that  the  first  separation  of  crystals  from  a  12J  per  cent 
salt  solution  occurs  at  —  9.5°  C.  (This  temperature  corresponds 
to  the  point  of  intersection  /?  of  the  dotted  line  with  a  line  drawn 
parallel  to  the  temperature  axis  through  a  point  12£  concentra- 
tion units  distant  »from  the  point  c  of  the  curve  for  pure  water.) 
The  dotted  horizontal  line  joining  the  eutectic  halting  points 
signifies  in  this  particular  instance  (typical  of  its  general  signifi- 
cation) that  a  halting  point  must  appear  at  —22.4  degrees  and 
continue  (provided  the  cooling  refers  to  100  grams  of  solution) 
throughout  a  period  of  time  which  is  the  arithmetical  mean 
of  the  periods  actually  observed  in  the  preceding  (10  per  cent) 
and  following  (15  per  cent)  solutions.  In  the  selfsame  manner, 
we  learn  that  the  first  salt  crystals  will  separate  from  a  27 £  per 
cent  salt  solution  at  +60  degrees,  corresponding  to  the  point  /?', 
and  that  eutectic  crystallization  will  also  occur  at  —22.4  degrees. 
The  steep  ascent  of  the  curve  fy?'  indicates  that  the  solubility  of 
common  salt  in  water  increases  only  slightly  from  0  to  100°  C. 

Thus,  the  answer  to  any  question  which  may  be  proposed 
relative  to  the  process  of  solidification  in  an  aqueous  solution  of 
common  salt  of  any  concentration  lies  in  Fig.  9a,  provided  such 
concentration  is  within  the  range  investigated.  To  reiterate, 
this  result  was  secured  by  arranging  the  cooling  curves  in  such 
a  manner  that  the  distances  between  their  first  breaks  are 
proportional  to  the  concentration  differences  between  the  respec- 
tive mixtures.  But  we  may  proceed  to  simplify  this  represen- 
tation by  omitting  the  cooling  curves  entirely,  and  retaining 
only  the  dotted  curves  and  the  eutectic  horizontal  in  our  figure. 
Fig.  9b  represents  a  modification  of  this  sort.  In  this  figure, 
which  is  known  as  a  fusion  diagram,  the  time  axis  is  lacking; 
the  axis  of  abscissas,  which  was  previously  used  in  this  connec- 
tion, has  now  become  the  concentration  axis,  along  which  the 
percentage  salt  content  of  the  solution  is  entered.  The  axis  of 


48  THE  ELEMENTS  OF  METALLOGRAPHY. 

ordinates  continues  as  temperature  axis.  Thus,  every  point  in  our 
present  co-ordinate  system  corresponds  to  a  mixture  of  common 
salt  and  water  of  definite  concentration,  and  at  definite  tempera- 
ture; the  point  a  for  example,  corresponding  to  a  mixture  of 
concentration  Qe  —  11.25  per  cent  NaCl,  at  the  temperature 
ae  =  +10  degrees.  The  curve  branches  A  B  and  BC,  which 
correspond  to  the  dotted  curve  branches  of  Fig.  9a,  were  obtained 
by  entering  the  breaks  b  from  the  cooling  curves  (corresponding 
to  the  temperature  of  separation  of  a  single  crystalline  variety) 
every  observed  concentration  in  the  co-ordinate  system,  and 
for  joining  these  points  by  a  continuous  curve.  The  eutectic 
horizontal  was  obtained  in  like  manner,  by  joining  the  several 
eutectic  halting  points,  all  of  which  lie  at  one  temperature 
(—22.4  degrees). 

This  simplified  diagram  is  equally  capable  of  furnishing  those 
who  are  well  versed  in  its  interpretation  with  complete  informa- 
tion on  any  question  concerning  the  state  of  aggregation  of  a 
salt  solution  of  any  concentration  at  any  temperature.  The 
beginner  usually  experiences  some  difficulty  in  becoming  accus- 
tomed to  this  method  of  representation,  but  those  who  have  over- 
come these  incipient,  moreover  trivial,  difficulties,  can  scarcely 
fail  to  recognize  its  inherent  desirability  —  we  may  even  say  its 
necessity.  When  conditions  are  complicated,  we  may  rest 
assured,  from  the  very  nature  of  affairs,  that  a  detailed  descrip- 
tion, covering  many  pages,  will  fail  to  render  a  clear  perception 
of  points  which  are  at  once  plainly  apparent  on  glancing  at  a 
diagram  of  this  sort.  It  therefore  appears  advisable  to  discuss 
the  simple  examples  which  we  shall  consider  first  in  great  detail, 
even  though  some  repetition  of  earlier  statements  may  be  un- 
avoidable. 

The  whole  area  bounded  by  the  co-ordinate  axes  (Fig.  9b)  is 
known  as  the  concentration-temperature  plane.  It  is  divided 
into  separate  " fields  of  condition"  (of  the  material  which  is 
existent  within  the  prescribed  limits),  or  simply  fields  (called 
variously,  areas,  regions,,  etc.),  by  the  curve  ABC  and  the  line 
DE.  Four  fields  are  to  be  differentiated  as  follows: 

Field  I  —  above  the  curve  branches  A  B  and  BC  —  is  known 
as  the  liquid  field,  since  every  mixture  of  common  salt  and  water 
which  exists  under  some  condition  of  concentration  and  tempera- 


TWO  COMPONENT  SYSTEMS.  49 

ture  given  by  a  point  located  within  this  field  is  a  homogeneous 
liquid,  when  in  a  condition  of  equilibrium.  For  example,  this  is 
true  of  the  above-mentioned  11.25  per  cent  salt  solution,  cor- 
responding to  the  point  a  (temperature  10°  C.). 

Field  II  —  below  the  eutectic  line  DE  —  is  known  as  the 
crystalline  field.  Any  common  salt-water  mixture,  the  concen- 
tration and  temperature  of  which  correspond  to  a  point  situated 
within  this  field,  is  entirely  solid,  consisting  of  two  crystalline 
varieties  (ice  and  salt).  Liquid  mixtures  are  incapable  of  exist- 
ence below  the  eutectic  horizontal  (provided  a  condition  of 
equilibrium  obtains). 

Field  III  —  within  the  triangle  ABD  —  answers  to  the  char- 
acterization, ice  +  solution.  Obviously,  any  mixture  located 
within  this  field  (abbreviated  phraseology  which  will  henceforth 
be  adopted  to  signify  mixtures  which  correspond  in  concentra- 
tion and  temperature  to  a  point  within  the  field)  can  neither 
exist  as  homogeneous  liquid,  nor  as  homogeneous  crystalline 
material,  but  rather  as  ice  and  solution.  (The  original  mixture, 
which  was  homogeneous  liquid  at  higher  temperatures,  has  sepa- 
rated on  crossing  the  boundary  into  this  field.) 

Field  IV  bears  close  analogy  to  Field  III  —  included  mixtures 
consist  of  salt  crystals  and  solution. 

Making  use  of  our  diagram,  the  following  assertions  may  now  be 
made  relative  to  the  changes  which  will  occur  on  continued  cool- 
ing of  a  solution  corresponding  to  the  point  a,  for  example 
(11.25  per  cent  NaCl,  10°  C.).  The  mixture  will  remain  liquid 
until  fall  in  temperature  brings  it  into  Field  III.  This  occurs 
on  passing  the  branch  AB,  i.e.,  at  a  temperature  of  —8°  C. 
(point  b,  where  the  crystallization  of  ice  begins),  and  our  mixture 
now  consists  of  pure  ice  and  a  salt  solution  which  becomes  more 
concentrated  as  the  temperature  falls,  until  this  solution  has 
reached  the  limiting  concentration  of  23  per  cent  salt,  at  —22.4 
degrees.  We  have  now  reached  the  eutectic  horizontal  DE, 
where  the  mixture  must  be  composed  of  ice  crystals,  salt  crystals, 
and  solution.  On  passing  DE,  the  crystalline  field  is  reached, 
wherein  our  mixture  must  consist  purely  of  ice  and  salt  crystals. 

The  salt  solution  represented  by  the  point  /  (26.25  per  cent 
NaCl,  75°  C.)  is  also  situated  within  the  liquid  field.  On  cooling, 
it  remains  liquid  until  the  branch  BC  is  crossed  and  Field  IV 


50  THE  ELEMENTS  OF  METALLOGRAPHY. 

entered.  Beginning  here,  the  mixture  is  composed  of  salt  crys- 
tals and  solution,  which  latter  becomes  less  concentrated  as  the 
temperature  falls,  until  it  has  reached  the  limiting  concentration 
of  23  per  cent  salt,  and  the  temperature  has  reached  that  of  the 
eutectic  horizontal  (just  as  in  the  above  case),  whereupon  ice 
appears  as  a  new  phase.  After  crossing  the  eutectic  horizontal,  no 
liquid  remains,  and  the  mixture  is  composed  entirely  of  salt  and 
ice  crystals. 

The  curve  ABC,  composed  of  the  two  branches1  AB  and  BC, 
is  called  the  fusion  curve',  it  joins  the*  points  of  initial  separation 
of  a  crystalline  variety  from  the  melts,  and  is  a  curve  of  incom- 
plete equilibrium.  The  branch  AB  corresponds  to  incomplete 
equilibrium  between  ice  and  salt  solution.  It  gives  the  tempera- 
ture at  which  the  first  separation  of  ice  occurs  in  any  concentra- 
tion between  0  and  23  per  cent  common  salt,  and  conversely  the 
salt  content  of  the  solution  which  is  in  incomplete  equilibrium 
with  ice  at  any  freezing  temperature.  The  equilibrium  repre- 
sented by  this  branch  is  called  incomplete,  for  the  reason  that 
the  concentration  of  a  phase,  the  solution,  in  this  case,  varies 
continuously  as  the  reaction  proceeds.  The  continuous  fall  in 
temperature  which  ensues,  follows  this  branch,  and  may  there- 
fore be  read  from  it.  This  may  be  made  clear  by  a  few  moments 
consideration  of  our  11.25  per  cent  salt  solution.  When  the 
temperature  has  fallen  to  b  =  —8  degrees,  the  point  of  inter- 
section of  a  vertical  drawn  (as  a  dotted  line)  at  right  angles  to 
the  concentration  axis  through  a,  with  the  branch  AB,  we  have, 
corresponding  to  b  in  our  co-ordinate  system,  a  mixture  of  salt 
and  water  of  concentration  11.25  at  a  temperature  of  —8  degrees. 
The  first  separation  of  ice  from  the  previously  homogeneous  solu- 
tion occurs  at  this  temperature.  If  we  should  now,  the  first 
trace  of  ice  having  appeared,  permit  no  change  in  the  tempera- 
ture of  our  system,  no  further  crystallization  could  occur,  since, 
on  separation  of  ice,  the  solution  becomes  more  concentrated,  and 
its  freezing  point  falls. 

This  is,  perhaps,  the  place  for  again  pointing  out  the  difference 
between  complete  and  incomplete  equilibrium.  If  we  are  deal- 

1  Sections  of  the  curve  which  are  distinguished  from  one  another  by  a  point 
(in  this  case  at  B)  where  the  direction  of  the  curve  is,  suddenly  changed  are 
termed  branches,  in  this  connection. 


TWO  COMPONENT  SYSTEMS.  51 

ing  with  complete  equilibrium,  replacing  the  salt  solution  by 
pure  water,  for  example,  we  may  bring  the  whole  system  at  will 
into  the  liquid  or  crystalline  condition  while  the  temperature 
remains  at  0°  C.,  or,  as  is  commonly  said,  we  may  conduct  the 
process  isothermally.  For  example,  in  order  to  completely 
freeze  the  system,  we  have  only  to  bring  it  into  a  chamber  where 
the  temperature  is  0  degrees,  and  provide  for  removal  of  the 
heat  which  will  be  liberated  during  the  ensuing  crystallization. 
Conversely,  pure  ice  may  be  completely  melted  at  0  degrees,  by 
in  some  manner  supplying  it  with  the  heat  which  must  be  ab- 
sorbed (bound)  during  fusion.  In  fact,  we  are  quite  unable  to 
impart  either  a  higher  or  lower  temperature  than  0  degrees  to  a 
system  composed  of  pure  ice  and  pure  liquid  water;  all  the  ice 
must  first  be  melted,  or  all  the  water  frozen  before  these  respec- 
tive effects  can  be  brought  about.  When  a  system  is  in  incom- 
plete equilibrium,  it  is,  on  the  contrary,  impossible  to  bring  about 
reaction  in  either  direction  at  constant  temperature,  under  con- 
stant pressure.  We  are  thus  unable  to  completely  freeze  the 
11.25  per  cent  salt  solution  at  —8  degrees,  even  though  care  be 
taken  to  remove  the  heat  liberated  during  crystallization:  the 
more  concentrated  solution  which  remains  after  the  first  crystal 
of  ice  has  separated  will  crystallize  no  further  until  some  tem- 
perature lower  than  —8  degrees  is  reached. 

Now,  complete  information  relative  to  the  manner  of  crystal- 
lization of  the  11.25  per  cent  salt  solution  is  supplied  by  the 
branch  AB  of  the  fusion  curve.  We  see,  on  considering  its 
course,  that  the  freezing  temperature  of  a  solution  will  have 
fallen  to  —9.5  degrees,  or  to  —12.2  degrees  when  this  solution 
has  reached  the  concentration  value  of  12^  per  cent,  or  of  15  per 
cent,  respectively,  owing  to  the  freezing  out  of  ice.  The  point 
B  (=  23  per  cent  NaCl,  and  -22.4°  C.)  is  the  end  point  of  thi3 
particular  curve  of  incomplete  equilibrium,  and  lies  upon  the 
eutectic  horizontal  DE,  at  which  location  complete  equilibrium 
characterizes  the  initial  appearance  of  salt  crystals. 

We  may  also  infer,  from  the  general  discussion  above,  that  our 
diagram  must  supply  information  concerning  the  quantitative 
relations  as  well.  It  is  at  once  apparent  that  questions  of  this 
nature  will  pertain  to  Fields  III  and  IV  only,  since  the  material 
in  Fields  I  and  II  is  completely  molten  or  crystalline,  respectively. 


52  THE  ELEMENTS  OF  METALLOGRAPHY. 

We  will  continue  to  abide  by  the  11.25  per  cent  salt  solution  as 
an  example,  and  propose  the  question,  What  amount  of  ice  has 
separated  from  the  solution  when  a  given  temperature,  say  —15 
degrees,  has  been  reached?  We  see  from  the  diagram  that  the 
concentration  of  a  solution,  and  indeed  the  only  solution,  which 
is  in  equilibrium  with  ice  at  —15  degrees,  amounts  to  18  per 
cent  NaCl  —  a  line  cd  drawn  parallel,  to  the  concentration  axis 
at  —15  degrees  cuts  the  branch  AB  at  the  point  d,  corre- 
sponding to  a  concentration  of  18  per  cent  NaCl.  Therefore, 
our  original  11.25  per  cent  solution  has  become  concentrated  up  to 
18  per  cent  at—  15  degrees,  and  in  answering  the  above  question 
we  need  only  calculate  how  much  water  must  be  removed  from 
an  11.25  per  cent  solution  to  make  it  an  18  per  cent  solution. 

Placing  the  initial  amount  of  solution  at  100  parts  by  weight, 
we  have  11.25  component  parts  of  salt,  from  which  62.5  parts  of 
18  per  cent  solution  may  be  made,  as  is  seen  from  the  following 
proportion:  n.25  :  x  =  18  :  100 

1125 
,  =  —=62.5. 

To  do  this,  37.5  parts  of  water  must  be  removed  in  the  form 
of  ice.  Our  11.25  per  cent  solution  has  therefore  separated  at 
—  15  degrees  to  37.5  per  cent  ice  and  62.5  per  cent  salt  solution 
of  concentration,  18  per  cent  NaCl. 

Thus,  the  fusion  diagram,  although  it  does  not  show  cooling 
curves,  renders  information  concerning  all  questions  which  per- 
tain to  the  state  of  aggregation  of  a  salt-water  mixture  of  any  con- 
centration, at  any  temperature  (atmospheric  pressure  being 
assumed).  Herein  is  included  the  condition  of  a  mixture  of  given 
concentration  at  all  stages  of  cooling  (represented  by  the  points 
of  a  line  drawn  parallel  to  the  temperature  axis  at  the  correspond- 
ing concentration  value).  The  relative  quantities  of  eutectic1 
in  the  completely  solidified  mixtures  of  each  and  every  concen- 
tration may  also  be  deduced  from  the  diagram.  At  concen- 
tration B  (  =  23  per  cent),  where  the  whole  alloy  is  crystallized  as 
eutectic,  this  quantity  is  unity  (1).  It  is  clear  that  the  same 

D 

amount  of   solution  of  concentration  —  (  =  11.50  per  cent)  can 

1  By  relative  quantity,  or  simply  quantity,  of  eutectic  is  meant  a  quantity 
referred  to  unit  weight  of  substance,  or  the  actual  quantity  of  eutectic  divided 
by  the  total  weight  of  substance. 


TWO  COMPONENT  SYSTEMS.  53 

yield  only  half  as  much  of  a  23  per  cent  solution,  i.e.,  that  the 
quantity  of  eutectic  in  a  mixture  of  this  sort  amounts  to  one- 
half.  In  general,  the  relative  quantity  of  eutectic  for  any  con- 
centration —  B,  between  0  and  B,  is  equal  to  — ,  where  —  <  1 
n  n  n 

by  assumption  (viz.,  the  respective  concentration  must  actually 
lie  between  0  and  B\  In  accord  with  this  generalization,  the 
quantity  of  eutectic  at  the  concentration  0  (pure  water)  is  also 
0.  A  relation  of  this  sort  is  said  to  be  linear,  and  we  make  the 
general  assertion:  the  relative  quantity  of  eutectic  is  a  linear 
function  of  the  concentration  for  all  concentrations  between 
0  and  23  per  cent.  This  condition  of  affairs  is  brought  into 
prominence  in  the  diagram  by  the  erection  of  verticals  upon  the 
concentration  axis  as  base,  at  lengths  which  are  made  pro- 
portional to  the  relative  quantities  of  eutectic  in  the  different 
concentrations.  A  line  joining  the  end  points  of  these  verticals 
is  straight  (hence  the  term  linear)  and  cuts  the  base,  or  concen- 
tration axis,  at  0  per  cent  (pure  water).  An  analogous  relation- 
ship must  hold  for  the  concentrations  which  are  beyond  B:  in 
this  region  as  well,  the  quantity  of  eutectic  must  decrease  lineally 
from  a  maximum  of  1  at  B,  to  0  at  concentration  100  (pure 
salt). 

If  the  experiments  are  conducted  with  uniform  amounts  of 
substance  throughout  the  whole  range,  the  heat  quantities 
liberated  during  eutectic  crystallization  and  the  lengths  of  the 
eutectic  halting  periods  upon  the  cooling  curves  as  well  (assum- 
ing uniformly  ideal  cooling  conditions  — see  p.  17)  must  actually 
appear  as  linear  functions  of  the  concentration. 

It  would  seem  superfluous  to  make  such  special  entry  in  the 
diagram  of  the  quantities  of  eutectic  pertaining  to  the  several 
concentrations,  since  these  quantities  are  given  by  the  diagram  in 
any  case.  Direct  observation  of  the  lengths  of  the  eutectic  halt- 
ing points  is,  however,  of  the  greatest  assistance  in  perfecting  the 
fusion  diagram,  as  was  first  shown  by  TAMMANN1,  and  we  shall, 
therefore,  consistently  follow  this  plan. 

1  TAMMANN,  Uber  die  Ermittelung  der  Zusammensetzung  chemischer  Ver- 
bindungen  ohne  Hilfe  der  Analyse,  Z.  anorg.  Chem.,  37,  303  (1903) ;  Die 
Anwendung  der  thermischen  Analyse  in  abnormen  Fallen,  Z.  anorg.  Chem., 
45,  24  (1905);  Uber  die  Anwendung  der  thermischen  Analyse  III,  Z.  anorg. 
Chem.,  47,  289  (1905). 


54  THE  ELEMENTS  OF  METALLOGRAPHY. 

Our  fusion  diagram  of  the  system  salt-water  is  incomplete,  in- 
asmuch as  it  does  not  extend  beyond  the  concentration,  30  per 
cent  NaCl.  This  is  due  to  the  fact  that  it  is  not  possible,  in  view 
of  the  low  boiling  point  of  water,  to  investigate  higher  concentra- 
tion under  atmospheric  pressure. 

2.  QUANTITATIVE  RELATIONS  ON  DISINTEGRATION  INTO  Two 
PHASES.  (THE  LEVER  RELATION.)  —  From  our  knowledge  of  the 
concentrations  c  and  d  of  the  two  phases  composing  a  salt-water 
mixture  g  in  the  equilibrium  condition,  which  information  was 
obtained  directly  from  the  fusion  diagram,  Fig.  9b,  we  were  able 
to  draw  an  accurate  conclusion  concerning  the  quantitative  rela- 
tionship between  these  two  phases.  We  will  now  proceed  to 
discuss  the  general  case.  Let  the  system  be  composed  of  the  two 
substances  A  and  B,  and  let  all  concentrations  be  expressed  in 
weight  per  cent  B.  A  mixture  of  concentration  b  will  then  contain 
b  grams  of  the  substance  B  in  100  grams  total  weight.  Sup- 
pose that  such  a  mixture  is  incapable  of  existence  in  a  homo- 
geneous condition  at  the  temperature  t,  but  be  separated  into 
two  phases  of  the  respective  concentrations  a  and  c.  Our  prob- 
lem is  to  ascertain  the  ratio  ~  of  the  quantities  of  these  two 

Qc 

phases. 

We  make  use  of  the  graphical  method  recently .  discussed  in 
depicting   this   relationship  —  Fig.    10.      The    axis    of   abscissas 
serves    as   concentration    axis;    along 
this  axis  we  enter  the  percentage  con- 
tent   of   the    mixture   in    B    progres- 
sively from   left  to    right.     The  per- 
centage   content   in   A    is    of    course 
fixed   at   the    same    time.     The    con- 
centration 0  signifies  pure  A,  and  the 
concentration  100,  pure  B.     The  axis 

of  ordinates  is  again  chosen  as  tern-          Concentration  in  weight* 
perature  axis,  centigrade  temperatures  per  cents, 

being     entered      progressively      from  FIG.  10. 

bottom    to    top.     (For    the    sake    of 

clearness,   temperature    axes    are   usually   erected   at   both   end 
points  of  the  concentration  axis.) 

Let  the  total  quantity  of  mixture  be  100  grams.     If,  then,  x 


t 


.100 


TWO  COMPONENT  SYSTEMS.  55 

grams  of  the  phase  of  concentration  a  are  present  in  a  condition 
of  equilibrium,  the  quantity  of  the  complimentary  phase  of  con- 
centration c  is  (100  —  x)  grams. 

Now,  the  x  grams  of  the  phase  of  concentration  a  contain 

a  grams  of  the  substance  B, 

and  the  (100  —  x)  grams  of  the  phase  of  concentration  c  contain 
100  -x 


100 


c  grams  of  the  substance  B. 


But  the  total  quantity  of  the  substance  B  is  given  by  the  per- 
centage content  b  of  the  original  (inhomogeneous)  mixture, 
multiplied  by  the  total  weight  of  the  latter,  which  was  assumed  to 
be  100  grams  (b  per  cent  of  100  =  b).  Whence  we  write, 

x  100  -  x 

a  H c  =  b. 

100  100 

From  this,  we  obtain  for  the  quantity  x  of  the  phase  a,  in 
grams  per  100,  viz.,  the  percentage  quantity  of  phase  a, 

c  -  b 

x  =  100  —  -  =  Qa, 
c  —  a 

.  and  for  the  percentage  quantity  100  —  x  of  the  phase  c, 

100  -x  =  100  -^=QC. 
c  —  a 

These  two  equations  yield  the  relation, 
Qa      c  —  b      be 
Qc      b  —  a      ab 

which  signifies  that  the  concentration  difference  c  —  b  is  equiva- 
lent to  the  distance  be  in  the  diagram,  and  the  difference  b  —  a 
equivalent  to  the  distance  ab. 

Considering  abc  as  a  lever  with  its  fulcrum  at  6,  and  imagin- 
ing masses  equivalent  to  Qa  and  Qc  suspended  at  the  end  points 
a  and  b  respectively,  we  have  the  well-known  equilibrium  condition, 

Qa.ab  =  Qc.bc. 


56  THE  ELEMENTS  OF  METALLOGRAPHY. 

Separation  of  the  mixture  b  has,  then,  progressed  in  accord- 
ance with  the  above  proportion.  We  shall  make  extended  use 
of  this  simple  relation  in  the  following  pages  under  the  name 
"lever  relation." 

3.  GENERAL  CASE.  —  Let  it  be  granted  that  we  are  dealing 
with  two  substances  A  and  B,  and  for  the  sake  of  simplicity  let 
these  be  considered  as  elements.  Moreover,  let  A  and  B  denote 
their  respective  melting  points  in  degrees  centigrade  as  well. 
We  shall  proceed  under  the  primary  assumptions:  (1)  that  the 
two  elements  are  completely  miscible  in  the  liquid  state,  but  com- 
pletely immiscible  in  the  crystalline  state;  (2)  that  they  show  no 
polymorphous  transformations;  and  (3)  that  they  form  no  chemi- 
cal compounds  with  one  another.  It  is  our  present  object  to 
become  familiar  with  the  fusion  diagram  representing  this  case. 
Concentrations,  in  weights  per  cent  B,  and  temperatures,  in 
degrees  centigrade,  are  entered  in  Fig.  lla,  in  the  usual  manner. 

When  a  small  quantity  of  B  is  dissolved  in  a  large  quantity  of 
A,  and  the  mixture  allowed  to  crystallize,  it  is  A  which  first  crys- 
tallizes—  pure  A,  in  accordance  with  our  previous  assumption  of 
immiscibility  in  the  crystalline  state.  According  to  the  law  of 
freezing-point  depression,  this  separation  commences  at  some 
temperature  below  the  melting  point  of  pure  A.  Moreover,  it 
does  not  proceed  at  constant  temperature,  since  we  are  here  deal- 
ing with  a  condition  of  incomplete  equilibrium.  On  the  contrary, 
in  order  that  A  may  continue  to  crystallize,  it  is  necessary  for 
the  temperature  to  drop  continuously.  During  the  process,  the 
melt  which  remains  in  equilibrium  with  pure  A  crystals  becomes 
continually  richer  in  B.  This  condition  has  already  been  dis- 
cussed at  length,  relative  to  crystallization  of  an  aqueous  solu- 
tion of  common  salt,  and  leads  to  the  conclusion  that  the  first 
separation  of  A  must  take  place  at  a  temperature,  the  value  of 
which  decreases  in  proportion  as  the  addition  of  B  increases. 
Thus,  when  we  enter  the  temperatures  of  initial  separation  of  A 
from  melts  of  varying  concentrations  in  our  co-ordinate  system 
and  join  these  points  continuously,  we  obtain  a  curve  which 
drops  to  lower  temperatures  as  the  B  concentration  increases. 
Let  this  curve  be  represented  by  AX  in  the  figure  (lla). 

A  and  B  are  the  two  independent  constituents  of  our  system, 
and,  as  such,  are  on  a  plane  of  equality.  The  melting  point  of  B 


D 


^ 

X 

i 

He« 

/ 

// 

A+Melt 

N 

\ 

/ 

'III 
B+Melt 

\ 

V 

r/  1 

IV 

A+Eu 

*Vl 

tectic 

!      /vj 

1  B+Eutect 

c 

St—  -T-  " 

—  r~ 

"  —  i  —  "i 

6: 

n- 

J                 20                40                6 
Concentration  in  Weigh 

i    . 

.  n.                                        m 

0                80              10(1 
t  per  cent  £ 

! 

E 


(57) 


Time 
FIG.  lla  and  FIG.  lib. 


58         THE  ELEMENTS  OF  METALLOGRAPHY. 

will  also  be  lowered,  in  accordance  with  the  law  of  freezing-point 
depression,  on  addition  of  A.  Thus,  if  we  add  a  small  quantity 
of  A  to  a  large  quantity  of  B,  and  permit  the  mixture  to  crystal- 
lize, B  will  begin  to  separate  at  some  temperature  below  its  melt- 
ing point,  but  will  fail  to  continue  to  separate  if  the  temperature 
is  kept  constant  —  the  same  general  condition  of  affairs  as  was 
noted  relative  to  dilute  solutions  of  B  in  A.  The  melting  point  of 
B  continues  to  fall  as  the  additions  of  A  increase,  and  conse- 
quently, a  curve  joining  the  temperatures  of  initial  separation  of 
B  from  melts  of  varying  concentrations  drops  to  lower  tempera- 
tures as  the  A  concentration  increases,  or  as  the  B  concentration 
(which  we  have  adopted  as  a  basis  for  calculations)  decreases. 
Let  this  curve  be  represented  by  BY. 

The  two  curves  AX  and  BY,  whereon  are  located  the  points 
corresponding  to  equilibrium  between  melt  and  the  crystalline 
varieties  A  and  B,  respectively,  intersect  at  some  point  C  of  our 
concentration-temperature  diagram,  which  must,  in  any  case,  be 
situated  below  the  melting  points  of  the  two  components.  At 
this  point  of  intersection,  since  it  constitutes  a  point  of  both 
curves,  both  crystalline  varieties  (A  and  B)  must  be  in  equilib- 
rium with  the  melt.  The  following  may  be  said  relative  to  the 
behavior  of  the  melt  of  composition  corresponding  to  the  point 
C:  At  all  temperatures  above  C,  the  melt  is  entirely  liquid, 
since  the  curves  AX  and  BY,  which  join  the  temperatures  of 
initial  separation  of  a  crystalline  variety,  are  not  met  until  the 
temperature  C  is  reached.  But  when  the  temperature  has  finally 
fallen  to  C,  both  curves  are  passed  simultaneously.  Separation 
of  both  varieties  at  once  must,  therefore,  occur  at  C  (assuming 
that  equilibrium  obtains);  moreover,  in  such  a  proportion  that 
the  composition  of  the  liquid  remains  unchanged. 

To  make  the  matter  still  clearer:  the  melt  of  composition  C  is 
in  equilibrium  with  both  crystalline  varieties  at  the  temperature  C, 
in  other  words,  it  is  saturated  with  both  substances.  Consequently, 
separation  of  a  definite  quantity  of  the  substance  A,  that  is, 
decrease  in  the  quantity  of  solvent  for  B  (A  may  be  regarded  as 
solvent  for  B}  to  a  given  extent  must  bring  about  separation  of  a 
corresponding  quantity  of  B,  and  conversely.  Thus,  we  are 
again  dealing  with  a  condition  of  complete  equilibrium,  —  as 
crystallization  proceeds,  the  quantities  of  both  crystalline  varie- 


TWO  COMPONENT  SYSTEMS.  59 

ties  increase  and  the  quantity  of  melt  decreases,  but  no  one  of 
the  phases  changes  its  composition.  In  effect,  the  melt  of  compo- 
sition corresponding  to  C  solidifies  at  the  temperature  corres- 
ponding to  C,  after  the  manner  of  a  pure  substance.  It  is  now 
plainly  evident  that  the  point  C  represents  the  eutectic  mixture 
of  A  and  B. 

The  fact  that  the  melting  point  of  a  pure  substance  may  not  be 
lowered  beyond  a  certain  limit  by  addition  of  a  second  substance 
(which  we  were  content  to  regard  on  p.  40  in  a  purely  experi- 
mental light)  now  appears  as  an  inevitable  consequence  of  the 
melting-point  depression  of  both  components.  Presupposing  a 
condition  of  equilibrium,  the  existence  of  a  liquid  (or  even  par- 
tially liquid)  mixture  of  A  and  B  at  a  lower  temperature  than 
that  corresponding  to  C  is  not  possible.  Nevertheless,  the 
dotted  continuation  of  both  curves  beyond  C  is  of  a  certain 
practical  significance.  It  is  not  infrequently  observed  on  cooling 
curves  that  separation  of  the  second  crystalline  variety,  which 
should  commence  at  C,  is  subject  to  retardation,  whereby  such 
continuation  of  one,  or  even  both,  of  the  curves  becomes  descrip- 
tive of  actual  conditions.  All  such  systems,  however,  constitute 
supercooled  or  unbalanced  systems,  which  will,  after  a  time, 
undergo  spontaneous  transformation  into  the  stable  condition, 
with  attendant  rise  in  temperature.  We  shall  continue  to  dis- 
regard these  phenomena  of  supercooling. 

To  summarize,  then,  our  diagram  supplies  the  following  infor- 
mation: 

(1)  All  melts  of  concentrations  between  0  and  C,  on  solidifica- 
tion, first  separate  pure  A,  becoming  progressively  richer  in  B 
with    falling     temperature,    until    what    remains    of    them    has 
attained  the  eutectic   composition   C.     These  residual  amounts 
then  crystallize  at  the  constant  temperature  C. 

(2)  All  melts  of  concentrations  between  C  and  100,  on  solidi- 
fication, first  separate  pure  B,  becoming  progressively  richer  in 
B  with  falling  temperature,  until  what  is  left  has  likewise  attained 
the  eutectic  composition  C;   whereupon   crystallization  ensues  at 
constant  temperature,  as  before. 

(3)  A  melt  of  concentration  C  crystallizes  at  constant  tempera- 
ture, yielding  A  and  B  simultaneously,  in  the  proportion  given 
by  C.     The  eutectic  horizontal  DE  passing  through  the   eutec- 


60  THE  ELEMENTS  OF  METALLOGRAPHY. 

tic  point  C,  and  extending  throughout  the  whole  concentration 
range,  signifies  that  eutectic  crystallization  occurs  in  all  mix- 
tures of  A  and  B.  As  to  the  relative  quantities  of  eutectic,  a 
maximum  (unit  quantity)  obtains  at  the  concentration  C,  since 
the  whole  melt  crystallizes  eutectically  at  this  concentration,  and 
zero  values  obtain  at  the  concentrations  0  and  100,  since  the 
eutectic  is  of  necessity  a  mixture.  For  concentrations  between 
0  and  C,  this  quantity  (of  eutectic)  is  proportional  to  the  B-con- 
tent,  and  for  concentrations  between  C  and  100,  it  is  proportional 
to  the  A-content  since,  in  the  first  case,  where  A  is  the  first  sub- 
stance to  crystallize,  the  whole  initial  quantity  of  B,  and  in  the 
second  case,  where  B  is  the  first  substance  to  crystallize,  the 
whole  initial  quantity  of  A,  remains  in  the  liquid  condition  up 
to  the  eutectic  point,  and  is  therefore  utilized  in  the  formation 
of  eutectic.  The  quantity  of  eutectic  must,  then,  decrease 
lineally  from  concentration  C  to  concentration  0  (pure  A),  and 
in  like  manner  from  concentration  C  to  concentration  100 
(pure  B).  This  is  shown  in  the  diagram,  according  to  the  method 
previously  described:  Verticals  are  erected  upon  the  concentra- 
tion axis  as  base,  in  such  manner  that  their  lengths,  for  the  vari- 
ous concentrations,  are  proportional  to  the  quantities  of  eutectic 
in  these  respective  concentrations.  As  is  apparent,  these  quan- 
tities reach  a  maximum  value  at  C.  On  joining  the  end  points  of 
these  verticals,  two  straight  lines  are  obtained,  one  intersecting 
the  concentration  axis  at  0  per  cent,  and  the  other,  at  100  per 
cent. 

When  equal  amounts  of  substance  are  used  in  determining 
each  of  the  cooling  curves,  the  heat  quantities  liberated  during 
eutectic  crystallization  are  proportional  to  the  lengths  of  these 
verticals.  Furthermore,  if  cooling  is  conducted  in  all  cases  in 
uniform  manner  —  based  upon  the  cooling  conditions  which  we 
have  assumed  to  be  ideal  —  the  lengths  of  the  eutectic  halting 
points  which  appear  on  the  cooling  curves  will  also  be  propor- 
tional to  the  lengths  of  these  verticals. 

(4)  The  attainment  of  a  zero  value  for  the  eutectic  at  concen- 
trations 0  and  100  constitutes  in  itself  an  expression  of  the  fact 
that  the  pure  substances  A  and  B  crystallize  at  constant  tempera- 
ture. 

It  is  clear  that  the  inverse  process  of  constructing  cooling 


TWO  COMPONENT  SYSTEMS.  61 

curves  from  our  diagram  may  be  carried  out,  provided  we  know 
the  melting  points  of  both  components  A  and  B,  as  well  as  their 
heat  of  mixture.  For  this  purpose,  information  relative  to  con- 
ditions of  cooling,  temperature  of  convergence,  etc.,  must  also  be 
at  hand.  In  Fig.  lib,  an  approximate  picture  of  cooling  curves 
of  the  two  pure  substances  and  of  four  intermediate  concentra- 
tions is  given  under  the  assumption  that  the  latent  heat  of  fusion 
is  approximately  the  same  for  both  substances,  and  that  the 
heat  of  mixture  is  negligible.  The  cooling  curves  are  again 
arranged  in  such  manner  that  the  distances  of  the  initial  breaks 
from  one  another  are  proportional  to  the  concentration  differences 
for  the  respective  curves.  Conversely,  it  may  of  course  be  seen 
from  this  example  in  what  manner  the  fusion  diagram  is  built  up 
from  the  individual  cooling  curves,  which  are  directly  obtained 
by  experiment. 

The  fusion  curve  A CB,  (Fig.  lla),  which  joins  the  temperatures 
of  initial  separation  of  a  single  crystalline  variety,  is,  as  we  are 
well  aware,  a  curve  of  incomplete  equilibrium.  The  variety  A 
separates  along  the  branch  AC.  From  the  course  of  the  curve,  we 
deduce  the  particular  temperature  at  which  a  melt  of  given  con- 
centration is  in  equilibrium  with  crystalline  A,  and  similarly,  the 
concentration  of  the  particular  melt  which  is  in  equilibrium  with 
crystalline  A  at  a  given  temperature;  in  other  words,  the  concen- 
tration of  a  melt  which  will  begin  to  crystallize  at  this  tempera- 
ture. Analogous  relations  hold  for  the  branch  BC,  along  which 
the  variety  B  separates.  Complete  equilibrium  between  the  two 
crystalline  varieties  A  and  B  and  the  melt  of  composition  C, 
prevails  along  the  eutectic  horizontal  DE. 

The  concentration-temperature  diagram  is  divided  into  four 
fields  of  condition  by  the  fusion  curve  and  the  eutectic  horizon- 
tal: 

Field  I,  above  the  fusion  curve  ACB,  is  the  field  of  homogene- 
ous liquid  material,  or  simply,  of  melt. 

In  Field  II,  represented  by  the  triangle  ACD,  the  separated 
crystalline  variety  A  is  found  in  equilibrium  with  melt  along  the 
branch  AC.  (This  phraseology  is  intended  to  suggest,  in  as  few 
words  as  possible,  the  concentration  changes  of  the  melt  for 
falling  temperature.)  Questions  concerning  the  quantity  of  sepa- 
rated A  and  the  quantity  of  melt,  which  are  together  in  equilib- 


62  THE  ELEMENTS  OF  METALLOGRAPHY. 

rium  at  any  chosen  point  within  the  field,  are  answered  by 
application  of  the  lever  relation  (see  p.  54). 

In  Field  III,  represented  by  the  triangle  BCE,  the  crystalline 
variety  B,  separating  along  the  branch  BC  is  found  in  equilibrium 
with  melt. 

Field  IV,  below  the  eutectic  horizontal  DE,  is  the  field  of  homo- 
geneous crystalline  material,  and  includes  the  two  crystalline 
varieties  A  and  B.  This  field  is  divided  into  two  sections,  IVl 
and  IV2,  by  a  line  Ce  drawn  through  C  (rendered  prominent  by 
means  of  cross  dashes)  parallel  to  the  temperature  axis.  Such 
division  corresponds  to  differences  in  structure  which  are  appar- 
ent on  microscopical  examination  of  the  completely  solidified 
alloys,  viz.,  those  located  below  DE,  or  in  Field  IV  of  our  diagram. 
Discussion  of  microscopical  investigation,  which  for  experimental 
reasons  is  adapted  to  the  completely  solidified  alloys  alone  (in 
measure  dependent  on  their  individual  nature),  is  reserved  for 
subsequent  pages. 

In  effect,  then,  the  eutectic  is  regarded  as  an  individual  struc- 
ture element  in  all  metallographical  investigations.  When  not 
too  highly  magnified,  it  is  generally  homogeneous  in  actual  appear- 
ance. Only  when  higher  powers  are  used,  does  it  become  appar- 
ent that  two  different  crystalline  varieties  are  concerned  in  its 
make-up.  It  is  noticeable  that  these  individual  constituents  of 
the  eutectic  are  very  often  arranged  side  by  side  in  a  finely 
lamellar  form,  or  in  the  form  of  irregular  grains.  The  reason  for 
this  apparent  homogeneity  is  not  difficult  to  discover  when  we 
inquire  closely  into  the  manner  of  crystallization  of  the  eutectic. 
For,  as  soon  as  the  least  quantity  of  A  has  separated,  the  melt  is 
supersaturated  with  respect  to  B,  and  therefore  permits  immedi- 
ate separation  of  a  corresponding  quantity  of  B.  A  and  B  thus 
occur  side  by  side  in  minute  crystals. 

Now,  on  the  A -rich  side,  i.e.,  in  concentrations  intermediate 
between  0  and  C,  pure  A  has  first  separated  and  has  continued  to 
separate  up  to  the  point  where  the  melt  has  become  enriched 
sufficiently  in  B  to  correspond  with  concentration  C.  At  this 
point,  complete  eutectic  crystallization  takes  place.  Conse- 
quently, there  must  be  present  in  the  solidified  alloys  of  Field  IVlt 
primarily  separated  crystals  of  A,  imbedded  in  the  eutectic 
which  has  subsequently  crystallized.  Thus  Field  IVl  is  to  be 


TWO  COMPONENT  SYSTEMS.  63 

designated  as  the  field  of  Crystalline  A  and  Eutectic  when  we 
regard  the  latter  as  a  separate  and  distinct  structure  element. 
In  analogous  manner,  Field  IV 2  (situated  at  the  right  of  the 
line  Ce),  in  which  primarily  separated  B  crystals  surrounded  by 
eutectic  must  occur,  is  characterized  as  the  field  of  Crystalline 
B  and  eutectic. 

Proceeding  from  several  general  experimental  facts,  we  have  in 
the  last  few  paragraphs  derived  the  form  of  the  fusion  curve  for 
a  two  component  system,  where  the  two  substances  sustain  no 
polymorphous  transformation,  unite  to  form  no  chemical  com- 
pound, and  show  no  miscibility  with  one  another  in  the  crystalline 
state.  The  characteristic  properties  of  such  a  diagram  may  be 
summarized  as  follows: 

(1)  The  fusion  curves  consist  of  two  branches  only,  AC  and  BC. 

(2)  One  eutectic    horizontal,   passing    through    the  point  of 
intersection  C  of  the  two  branches  of  the  fusion  curve,  occurs. 

(3)  The  eutectic  horizontal  traverses  the  whole  diagram.     If, 
upon  the  concentration  axis  as  base,  verticals  are  erected  through- 
out  the   various   concentrations,   at  lengths   which   are   propor- 
tional to  the  relative  quantities  of  eutectic  in  these  respective 
concentrations,  and  the  end  points  of  these  verticals  joined,  two 
straight  lines,  which  intersect  with  one  another  at  C,  and  with  the 
concentration  axis  at  concentrations  0  and  100,  are  obtained. 

We  shall  see,  on  considering  other  cases  describing  the  mutual 
relations  of  the  elements,  that  a  fusion  diagram  of  this  type  is 
valid  for  a  two  component  system  only  when  the  above  assump- 
tions are  actually  realized. 

Now,  if  we  have  investigated  the  mutual  relations  of  two 
elements  by  the  method  of  thermal  analysis,  viz.,  by  taking 
cooling  curves  of  the  pure  elements  and  of  a  series  of  mixtures, 
say  from  10  to  10  per  cent  progressively,  and  if  we  find  that  the 
fusion  diagram  deduced  from  these  cooling  curves  reproduces  the 
characteristic  properties  of  the  diagram  which  we  are  now  con- 
sidering, the  following  inverse  conclusions  may  be  drawn: 

(1)  The  elements  exhibit  complete   miscibility  in  the  liquid 
state,  and  no  miscibility  in  the  crystalline  state. 

(2)  They  undergo  no   polymorphous  transformation,    at    least 
none  which  is  accompanied  by  a  sufficient  heat  effect  to  render  it 
apparent  under  the  given  conditions. 


64  THE  ELEMENTS  OF  METALLOGRAPHY. 

(3)  They  form  no  chemical  compounds  with  one  another; 
more  accurately,  they  fail  to  unite  with  one  another  under  the 
conditions  of  experiment  (namely,  on  being  fused  in  conjunction 
at  the  respective  temperature)  to  an  extent  which  may  be  ascer- 
tained thermally.  The  above  qualification  is  essential.  For,  in 
case  we  had  undertaken  to  work  up  the  fusion  diagram  for  liquid 
hydrogen  and  oxygen,  we  would  have  been  forced  to  a  conclusion 
on  the  basis  of  our  cooling  curves,  that  no  compound  of  these  two 
elements  exists.  In  reality,  non-appearance  of  the  compound 
under  these  conditions  is  merely  due  to  the  fact  that  the  reaction 
velocity  at  this  low  temperature,  and  even  at  ordinary  temper- 
ature (far  above  the  boiling  points  of  these  two  elements),  is  so 
trifling  that  appreciable  quantities  of  water  fail  to  be  formed. 
Obviously,  the  metals  are  not  exempt  from  entering  into  rela- 
tions of  this  sort.  TAMMANN  1  is  inclined  to  the  opinion  that  the 
aluminium-antimony  alloys  belong  in  this  category.  It  is  also 
possible  for  two  elements  to  form  a  compound  which  can  exist 
only  at  temperatures  even  lower  than  that  of  the  eutectic  point 
(see  Fig.  45,  p.  145). 

If,  then,  we  confine  our  reasoning  to  the  temperature  region 
throughout  which  our  investigation  is  extended,  the  conclusions 
drawn  from  the  fusion  diagram  are  binding.  It  may  be  noted, 
in  this  connection,  that  every  experimental  result  which  is  fol- 
lowed by  a  negative  conclusion  of  some  sort  (e.g.,  in  the  above 
instance,  affirmation  of  non-existence  of  a  compound)  implies 
certain  limitations  of  this  general  nature.  On  the  other  hand, 
positive  conclusions  (e.g.,  relative  to  the  existence  of  a  compound) 
are  subject  to  no  such  limitations. 

In  any  case,  however,  it  appears  desirable  to  test  the  evidence  of 
the  fusion  diagram,  however  unimpeachable  it  may  seem,  by 
some  independent  method.  The  most  valuable  method  available 
for  this  purpose  is  direct  investigation  of  the  structure  of  the 
solidified  alloys.  Great  importance  is  therefore  attached  to  this 
method.  The  structure  of  the  alloys  often  serves  as  a  key  to  the 
solution  of  all  questions,  particularly  when  the  results  of  thermal 
investigation  are  not  sufficiently  detailed  to  permit  construction 
of  a  diagram  which  shall  be  free  from  all  objection.  For  investi- 
gation of  this  sort,  the  solidified  reguli  are  ground  and  polished  to 
1  TAMMANN,  Z.  anorg.  Chem.,  48,  53  (1905). 


TWO  COMPONENT  SYSTEMS.  65 

a  mirror-like  surface.  At  times,  conclusions  may  be  drawn  on 
examination  of  the  polished  sections  before  they  have  been  sub- 
jected to  any  additional  treatment,  as  is  the  case  when  the  sepa- 
rate constituents  differ  in  color.  In  general,  after  polishing,  it  is 
necessary  to  apply  some  further  treatment  depending  upon  the 
different  chemical  behavior  of  individual  constituents,  such  as 
variable  resistance  to  the  action  of  certain  reagents  (etching), 
variable  susceptibility  to  oxidation  in  the  air  at  ordinary  temper- 
ature or  on  heating  (causing  them  to  tarnish),  etc.  The  naked 
eye  does  not  often  suffice  in  making  these  observations.  Usually 
a  suitable  microscope  must  be  brought  into  requisition. 

We  will  here  assume  the  choice  of  two  metals  A  and  B  which 
behave  differently  towards  a  certain  etching  agent,  A  with- 
standing its  action,  and  B  vigorously  attacked  by  it.  The  alloy 
sections  of  various  concentrations,  after  polishing  and  etching, 
are  illuminated  by  a  beam  of  light  which  is  made  to  fall  normally 
upon  their  polished  surface.  This  may  be  attained  by  using  a 
vertical  illuminator,  as  we  shall  see  later.  The  portions  of  the 
section  which  have  not  been  attacked  by  the  etching  agent  will 
have  retained  their  mirrored  surface,  and  will,  therefore,  com- 
pletely reflect  the  incident  light,  while  the  affected  portions, 
having  attained  a  rough  surface,  will  fail  to  reflect  the  light  to 
any  extent.  If,  then,  we  examine  the  section  through  a  micro- 
scope, the  axis  of  which  is  at  right  angles  to  the  surface  of  the 
section,  the  reflecting  portions  must  appear  light,  and  the  non- 
reflecting  portions  dark. 

Fig.  12a  is  intended  to  represent  a  section  composed  of  pure  A 
which  has  been  manipulated  in  the  above  manner.  The  struc- 
ture of  a  section  composed  of  a  single  structure  element  is  very 
often  difficult  to  develop.  Still,  it  is  in  general  possible  by  choice 
of  a  suitable  etching  agent  and  proper  treatment  to  bring  out  the 
boundaries  between  the  separate  polyhedrons  which  have  been 
formed  on  crystallization  of  the  melt.  This  polyhedral  configura- 
tion obviously  affords  a  polygonal  structure  at  the  plane  surface 
of  the  section.  In  general,  the  sharp  appearance  of  polygonal 
structure  is  traceable  to  small  quantities  of  some  relatively  non- 
resistant  impurity,  which  crystallizes  last  of  all,  and  therefore 
collects  between  the  individual  polygons,  where  it  is  affected  by 
the  etching  agent.  Thus  we  see  a  network  of  dark  lines  all  over 


66 


THE  ELEMENTS  OF  METALLOGRAPHY. 


TWO  COMPONENT  SYSTEMS.  67 

the  surface  of  our  section,  and  these  form  acute  angular  bound- 
aries of  the  bright  unattacked  crystalline  polygons.  These  poly- 
gonal cross  sections  through  the  crystals  are,  as  a  rule,  six-sided. 
Fig.  12f  represents  a  section  of  pure  B,  etched  in  the  same  manner. 
In  accordance  with  the  preassumed  slight  resistance  of  B  to  the 
action  of  the  etching  agent,  this  section  appears  etched  to  a  dark 
color.  It  is  quite  possible  to  discern  its  structure,  and  we  note 
the  appearance  of  irregular  crystalline  polygons  with  rounded 
corners. 

The  action  of  the  etching  agent  is  sometimes  particularly 
marked  at  certain  spots,  giving  rise  to  the  formation  of  local 
indentations  (Aetznapfchen).1  Fig.  12d  represents  a  section  com- 
posed of  60  per  cent  B  and  40  per  cent  A.  The  alloy  of  this  con- 
centration solidifies  completely  at  the  eutectic  temperature,  as 
may  be  seen  from  the  diagram,  Fig.  lla.  Accordingly,  we  now 
have  what  is  commonly  called  the  pure  eutectic  under  considera- 
tion, and  we  will  suppose  that  it  shows  the  previously  mentioned 
characteristic  lamellar  structure.  Interposed  light  and  dark 
striations  (the  former  corresponding  to  unetched  particles  —  con- 
sisting of  A ;  the  latter  to  etched  particles  —  consisting  of  B)  are, 
therefore,  to  be  seen.  We  are  unable  to  advance  any  reason  for 
the  development  of  this  remarkable  lamellar  structure.  Slow 
cooling  appears  to  favor  its  appearance.  However,  the  eutectic 
frequently  shows  a  more  or  less  finely  granular  structure,  which 
in  many  cases  occurs  alone,  but,  on  the  other  hand,  often  accompa- 
nies the  lamellar  structure. 

Fig.  12b  represents  a  section  composed  of  20  per  cent  B  and 
80  per  cent  A.  A  glance  at  the  diagram  serves  to  inform  us  that 
here  the  crystalline  variety  A  has  first  separated.  Accordingly, 
we  recognize  bright  angular  A  crystals  imbedded  (like  islands)  in 
the  lamellar  eutectic,  which  has  solidified  at  a  later  period.  The 
primarily  separated  A  crystals  show  included  eutectic  in  places, 
a  condition  which  frequently  occurs  in  practice  and  which,  under 
certain  circumstances,  renders  it  difficult  to  distinguish  between 
primarily  and  secondarily  separated  material. 

Fig.  12c,  which  is  intended  to  represent  a  section  consisting  of 
40  per  cent  B  and  60  per  cent  A,  must  offer  essentially  the  same 

1  These  might  be  called  in  English,  etch-holes,  or  etch-hollows  (Transla- 
tor). 


68  THE  ELEMENTS  OF  METALLOGRAPHY. 

picture  as  Fig.  12b,  since,  according  to  the  diagrammatic  evi- 
dence, the  crystalline  variety  A  has  also  separated  first  in  this 
case.  But,  while  the  A  crystals  make  up  two-thirds,  and  the 
eutectic  one-third,  of  the  total  quantity  of  the  first  alloy,  this 
proportion  has  become  reversed  in  the  present  alloy,  which  fact 
also  follows  from  the  diagram.  Consequently,  a  corresponding 
decrease  in  the  quantity  of  A  crystals  and  increase  in  the 
quantity  of  eutectic  is  to  be  seen  in  Fig.  12c  (compared  with 
Fig.  12b). 

Fig.  12e  represents  a  section  containing  80  per  cent  B.  Here 
B  has  separated  first  (as  shown  by  the  diagram),  and  we  find  the 
rounded  B  crystals,  which  have  been  vigorously  attacked  by  the 
etching  agent,  disposed  throughout  the  entire  eutectic.  This 
eutectic  in  no  wise  differs  from  that  which  has  crystallized  in  the 
other  concentrations.  The  diagrammatic  evidence  that  half  of 
the  alloy  of  concentration  80  per  cent  B  solidifies  eutectically  is 
corroborated  by  the  appearance  of  the  microscopic  picture  shown 
in  the  drawing,  Fig.  12e. 

We  may  now  offer  a  brief  summary  of  the  respective  pictures 
which  must  be  presented  by  the  sections,  provided  their  structure 
is  in  accord  with  the  specifications  of  the  diagram: 

(1)  The  quantity  of  eutectic  must  increase  steadily  from  con- 
centration 0  per  cent  B,  where  its  value  is  zero,  up  to  concentra- 
tion C  per  cent  B,  where  its  value  is  unity,  and  it  must  decrease 
from  this  latter   concentration  towards   concentration    100   per 
cent  B,  where  its  value  is  again  zero.     The  structure  of  the  eutectic 
must  in  all  cases  be  identical. 

(2)  The  crystals  which  have  separated  primarily  between  con- 
centrations 0  and  C  must  be  alike  among  themselves,  but  must 
differ  from  those  which  have  separated  primarily  between  con- 
centrations C  and  100,  and  which  are  also  alike  among  themselves. 
That   the  crystals   have    separated  primarily  is  apparent   from 
their  being  embedded  in  the  coherent  eutectic.     The  quantity  of 
a  crystalline  variety  which   has   separated   primarily  obviously 
decreases  in  proportion    as    the  quantity  of  eutectic  increases. 
(It  is  possible  for  both  crystalline  varieties  to  be  present  in  the 
vicinity  of  the  eutectic  point  C  as  primary  elements  when  super- 
cooling occurs.)1 

1  LEVIN,  Z.  anorg.  Chem.,  45,  31  (1905). 


TWO  COMPONENT  SYSTEMS.  69 

(3)  No  structure  element  aside  from  the  three  which  have 
been  discussed,  namely,  the  crystalline  varieties  A  and  B  and  the 
eutectic,  can  appear  in  the  sections. 

In  one  respect,  investigation  of  the  sections  carries  us  further 
than  thermal  investigation.  It  is  clear  that  the  eutectic  hori- 
zontal DCE  (Fig.  lla)  extends  throughout  the  whole  diagram, 
in  other  words,  that  the  quantity  of  eutectic  becomes  equal  to 
zero  at  the  precise  concentrations  0  and  100  (the  pure  sub- 
stances) only  when  there  is  absolutely  no  miscibility  in  the  crys- 
talline state.  If  A  is  capable  of  dissolving  a  certain  quantity  of 
B,  pure  A  crystals  will  not  separate  on  the  A-rich  side,  but, 
rather,  A  crystals,  which  have  dissolved  a  quantity  of  B.  The 
result  will  be  that  no  eutectic  can  appear  until  more  B  than  the 
A  crystals  can  dissolve  is  present  in  the  mixture.  Analogous  rela- 
tions hold  for  the  5-rich  side,  provided  the  B  crystals  are  possessed 
of  a  certain  tendency  to  dissolve  A.  In  such  cases,  then,  the 
eutectic  horizontal  fails  to  extend  throughout  the  whole  diagram, 
but  ends  on  the  A -rich  (left)  side  at  some  point  between  D  and 
Cj  and  on  the  B-rich  (right)  side  at  some  point  between  C  and  E. 
These  relations  will  be  discussed  in  greater  detail  later,  when 
miscibility  in  the  crystalline  state  is  taken  up.  At  present,  the 
only  question  at  issue  is:  What  are  the  limits  within  which  our 
assumption  of  immiscibility  in  the  crystalline  state  is  realized? 
Thermal  investigation  is  not  adapted  to  the  task  in  hand.  That 
is  to  say,  when  the  quantity  of  eutectic  has  become  very  small,  the 
period  of  constant  temperature  during  solidification  of  the  eutectic 
will  have  become  so  short  as  to  escape  observation  on  the  cooling 
curves.  Graphical  deduction  of  the  end  points  of  the  eutectic 
horizontal,  with  the  aid  of  the  eutectic  periods  throughout  an 
extended  concentration  range,  also  admits  of  uncertainty,  not 
infrequently  amounting  to  several  per  cent.  Microscopical  inves- 
tigation of  the  prepared  sections  carries  us  much  further  in  this 
respect.  //  there  is  actually  no  miscibility  in  the  crystalline  state, 
the  eutectic  cannot  fail  to  appear  on  very  slight  additions  (amounting 
to  less  than  one  per  cent)  of  B  to  A  and  of  A  to  B.  The  eutectic  may, 
in  general,  be  recognized  without  difficulty  by  its  characteristic 
lamellar  or  finely  granular  structure.  Investigation  of  electrical 
conductivity  —  to  be  discussed  later  —  may  perhaps  be  even 
better  suited  to  the  object  in  view. 


70  THE  ELEMENTS  OF  METALLOGRAPHY. 

In  concluding  this  section,  a  few  remarks  relative  to  the  gen- 
eral course  of  the  fusion  curve  ACB,  and  to  the  position  of  the 
eutectic  point  C,  may  be  offered.  As  long  as  the  quantity  of  one 
component  is  small  in  comparison  with  that  of  the  other,  viz.,  as 
long  as  we  are  dealing  with  so-called  dilute  solutions,  the  freez- 
ing point  depression  which  a  pure  substance  A  sustains  on  addi- 
tion of  a  given  quantity  of  a  second  substance  B,  when  complete 
miscibility  occurs  in  the  liquid  state  and  complete  immiscibility 
in  the  crystalline  state,  is  subject  to  simple  laws.  According  to 
van't  Hoff,  the  depression  depends,  on  the  one  hand,  on  the  prop- 
erties of  the  substance  A  which  plays  the  part  of  solvent;  it 
increases  in  proportion  as  the  melting  point  of  the  solvent  be- 
comes higher,  and  as  the  latent  of  fusion  becomes  less.  On  the 
other  hand,  it  depends  upon  the  added  substance  B  (dissolved), 
according  to  the  simple  law:  The  freezing  point  depression  is 
proportional  to  the  ratio  of  the  number  of  dissolved  molecules  to 
the  total  number  of  molecules.  Now,  investigations  by  RAMSAY, 
TAMMANN  and  HEYCOCK  and  NEVILLE  have  shown  that  the 
greater  number  of  metals  dissolve  in  a  monatomic  condition. 
Thus,  the  freezing  point  depression  caused  by  metals  in  their 
capacity  as  dissolved  substances  is  inversely  proportional  to 
their  atomic  weights.  This  relationship  between  freezing  point 
depression  and  atomic  weight  may  readily  be  shown,  as  is  done  in 
Fig.  13,  by  entering  the  composition  of  the  alloy  in  atomic 
per  cent,  instead  of  weight  per  cent,  on  the  axis  of  abscissas.1 

The  curve  branches  AX  and  BY  must  appear  as  straight  lines, 
as  long  as  the  laws  of  dilute  solutions  hold  (in  practice  up  to 
additions  of  5  to  10  atomic  per  cent).  The  subsequent  course  of 
these  two  branches  is  subject  to  great  diversity.  Very  often  (N.B. 
If  atomic  per  cents  are  entered  as  abscissas)  the  whole  course 
remains  rectilinear.  They  may  be  concave,  convex,  or  partly 
concave  and  partly  convex,  with  respect  to  the  concentration 
axis.  However,  these  branches  do  not  deviate  in  their  form  from 
a  straight  line  to  such  an  extent  as  to  render  it  impossible  to 

1  If  an  alloy  is  composed  of  p  weight  per  cent  of  the  element  A,  of  atomic 
weight  A,  and  q  weight  per  cent  of  the  element  B,  of  atomic  weight  B,  then 


its  A  -content  in  atomic  per  cent  is  -  fj-  ,  and  its  fi-content, 


TWO  COMPONENT  SYSTEMS. 


71 


draw  conclusions  concerning  the  position  of  their  intersection. 
Relative  to  the  position  of  the  point  of  intersection  C  of  the  two 
branches  AX  and  BY,  we  may  say  that  it  approaches  the  central 
point  between  A  and  B  and  also  becomes  lower  ceteris  paribus 
in  proportion  as  the  melting  points  A  and  B  approach  one 
another.  If,  however,  the  two  components  A  and  Bl  (Fig.  13) 
differ  considerably  in  melting  point,  the  point  of  intersection 
Cl  of  the  two  branches  AX  and  B^Y^  assumes  a  position  to- 
wards the  side  of  the  less  fusible  component  —  the  A  side. 
This  conclusion  is  generally  in  accord  with  the  experimental 
results. 

We  see  from  the  position  of  the  point  of  intersection  C2  of  the 
branches  AX  and  B2Y2,  also  shown  in  Fig.  13,  that  this  approach 
to  A  can  be  indefinitely  close,  whereby  we  are  confronted  by  the 
possibility  that  C  and  A  practically  coincide.  In  such  a  case, 


u 

'B  Crystals* Melt 


III 
B  Crystals  +A  Crystals 


Atomic  per  cent  B 
FiG.13. 


Weight  per  cent  £ 
FIG.  14. 


which  is  shown  in  Fig.  14,  the  eutectic  must  be  practically  iden- 
tical with  the  less  fusible  pure  substance  A.  Accordingly,  the 
following  relations  are  to  be  expected  on  crystallization  of  a 
molten  mixture  of  A  and  B:  The  less  fusible  crystalline  variety 


72  THE  ELEMENTS  OF  METALLOGRAPHY. 

B  separates  first  on  cooling  any  liquid  mixture  of  A  and  B  (any 
solution  of  A  and  B  in  one  another).  The  temperature  falls 
along  the  curve  of  incomplete  equilibrium  BA  until  all  B  has 
crystallized.  At  this  point,  the  melt  consists  entirely  of  pure  A, 
which  now  crystallizes  at  its  own  constant  melting  temperature. 
No  melting  point  depression  occurs,  then,  on  adding  B  to  A, 
because  melts  of  all  concentrations  first  of  all  separate  5. 
The  (eutectic)  horizontal  extends  to  pure  B,  since,  under  our 
preassumed  condition  of  immiscibility  in  the  crystalline  state  in 
all  concentrations  between  0  and  100  per  cent  B,  liquid  A  must 
be  present  up  to  the  very  last.  The  time  duration  of  this  "eutec- 
tic crystallization"  is  a  linear  function  of  the  quantity  of  A  in 
weight  per  cent,  provided  the  same  total  quantity  of  substance 
is  used  in  all  cases,  and  the  same  ideal  cooling  conditions  obtain. 
The  concentration-temperature  diagram  is  divided  into  three 
fields  of  condition.  Field  /,  above  the  curve  BA,  is  the  field  of 
liquid  or  melt.  Field  //,  represented  by  the  triangle  ABC, 
locates  the  equilibrium  between  crystalline  variety  B  and  melt 
composed  of  A  and  B.  Field  ///,  below  the  horizontal  AC, 
locates  the  completely  solidified  alloys,  all  of  which  consist  of  the 
primarily  separated  crystalline  variety  B,  surrounded  by  the  last 
separated  variety  A.  A  represents  the  eutectic  in  this  case,  and  the 
latter  can  show  only  one  structure  element  on  microscopic  exami- 
nation. 

4.  ANTIMONY-LEAD  ALLOYS.  —  In  concluding  section  A  (cf. 
p.  38)  we  will  discuss,  by  way  of  illustration,  the  actual  diagram 
of  the  system  Antimony-Lead.  In  view  of  the  preceding  expla- 
nation, a  glance  at  the  fusion  diagram  of  the  antimony-lead 
alloys,  according  to  ROLAND-GOSSELIN, J  Fig.  15,  will  suffice  to 
render  the  mutual  relations  of  these  two  metals  clear.  At  the 
outset,  we  see  that  antimony  and  lead  are  completely  miscible  in 
the  liquid  state  and  completely  immiscible  in  the  crystalline 
state.  We  learn  that  the  metals  undergo  no  polymorphous  trans- 
formations within  the  temperature  range  investigated,  at  least 
none  which  are  accompanied  by  noticeable  heat  effects,  and, 
finally,  we  perceive  that  the  metals  form  no  compounds  with  one 
another,  on  being  fused  in  conjunction.  As  to  details,  we  see 

1  ROLAND-GOSSELIN,  Contribution  a  l'6tude  des  alliages,  Paris  (1901),  p. 
104. 


TWO  COMPONENT  SYSTEMS. 


73 


that  the  melting  point  of  lead  was  found  to  be  326  degrees,  and 
that  of  antimony,  632  degrees.  Again,  the  composition  of  the 
eutectic  appears  as  13  weight  per  cent  antimony  +  87  weight 
per  cent  lead;  its  melting  point  as  228  degrees. 


800C 


600C 


400C 


.Pb 


Sb 


200C 


Eutectic 


Melt 


Sb  +  Melt 


£6+  Eutectic 


10 c     20      30       40      50      60       70 
Weight  per  cent  Antimony 


80      90 


FIG.  15.     Fusion  Diagram  of  Antimony-Lead  Alloys. 

It  should  be  noted,  in  this  connection,  that  the  diagram  was 
not  made  as  complete  by  the  author  as  is  shown  in  our  figure. 
He  gives  only  the  course  of  the  fusion  curve  ACB;  no  indication 
relative  to  the  extreme  concentrations  at  which  the  presence  of 
eutectic  is  revealed  by  the  cooling  curves  is  to  be  found  in 
his  paper.  On  this  score,  then,  we  are  not  justified  in  assuming 
complete  immiscibility  in  the  crystalline  state.  The  extension  of 
the  eutectic  horizontal  throughout  the  whole  diagram,  and  the 
erection  of  verticals  on  the  concentration  axis  proportional  to  the 
relative  quantities  of  eutectic,  would  appear,  thus  far,  to  be  a 
wholly  arbitrary  proceeding.  This  is  justified,  however,  by  the 
results  of  a  microscopical  investigation  of  prepared  sections  of  the 


74         THE  ELEMENTS  OF  METALLOGRAPHY. 

reguli  by  CHARPY.1  Charpy  certifies  to  the  following:  Sections 
containing  from  13  to  100  per  cent  antimony  show,  after  polishing, 
primarily  separated,  hard,  cubical  crystals  of  antimony,  sur- 
rounded by  eutectic,  both  constituents  of  which  may  be  ren- 
dered perceptible  by  weak  etching  with  nitric  acid.  The  quantity 
of  primarily  separated  antimony  crystals  increases  with  the 
antimony  content.  Sections  containing  from  0  to  13  per  cent 
antimony  (those  possessing  concentrations  located  at  the  left  of 
the  eutectic)  present  a  different  appearance;  they  are  difficult  to 
polish,  and  show  large  dendritic  crystals,  which  are  blackened  by 
hydrogen  sulphide  and  dissolved  by  nitric  acid,  imbedded  in  an 
eutectic  composed  of  two  structure  elements.  The  quantity  of 
these  dendrites,  which  in  all  probability  consist  of  pure  lead, 
increases  with  the  lead  content. 

The  structure  is  thus  in  complete  accord  with  the  evidence  of 
our  diagram.  It  is  true  that  Charpy  fails  to  state  in  particular 
that  the  eutectic  between  0  and  13  per  cent  antimony  is  identical 
with  that  between  13  and  100  per  cent  antimony,  and  yet  he  could 
scarcely  have  failed  to  remark  upon  any  observed  differences  in 
this  respect.  Again,  he  does  not  specify  the  minimum  additions 
of  antimony  to  lead,  and  of  lead  to  antimony,  which  yield  alloys 
wherein  the  eutectic  is  still  distinguishable.  Nevertheless,  we 
gather  from  his  statements  in  their  entirety  that  he  investigated 
a  large  number  of  concentrations,  doubtless  including  those  of 
very  low  and  very  high  antimony  content,  and  we  may  affect 
some  assurance  that  our  elaboration  of  the  diagram  has  been 
based  upon  inferences  which  are  in  the  main  correct. 

The  fields  of  condition  are  accordingly  characterized  as  follows: 
Above  ACB,  the  alloys  of  all  concentrations  exist  in  the  liquid 
condition  alone.  In  the  regions  bounded  by  the  fusion  curve 
and  the  eutectic  horizontal,  a  single  crystalline  variety,  more 
specifically  in  the  triangular  field  AC  a,  pure  lead,  and  in  the 
triangular  field  BCb,  pure  antimony,  is  found  in  equilibrium  with 
melt.  Below  the  eutectic  horizontal  aCb,  the  alloys  are  com- 
pletely solidified,  and  are  composed  of  the  two  crystalline  varie- 
ties, lead  and  antimony.  In  that  we  regard  the  eutectic  as  an 
individual  structure  element,  we  have,  at  the  left  of  the  dotted 
line  Cc,  a  field  of  primarily  separated  lead  crystals  and  eutectic, 

1  CHARPY,  Contribution,  p.  131. 


TWO  COMPONENT  SYSTEMS.  75 

and,  at  the  right  of  this  line,  a  field  of  primarily  separated  anti- 
mony crystals  and  eutectic. 

A  few  additional  examples  of  systems  embracing  two  metals  in 
which  the  components  presumably  exhibit  the  same  mutual 
behavior  as  do  antimony  and  lead  are  to  be  found  in  the  litera- 
ture. Unfortunately  nearly  all  of  the  respective  investigations 
are  impaired  by  a  lack  of  determinations  which  would  fix  the 
extent  of  the  eutectic,  or  by  a  lack  of  data  relative  to  such  work. 
Accordingly,  more  or  less  uncertainty  attaches  itself  to  all  con- 
clusions based  upon  the  material  which  is  generally  available, 
and  we  will  therefore  rest^content  with  the  above  choice  of  an 
example  which  is  itself  not  free  from  this  objection.1 

B.  Polymorphous  Transformations  do  not  Occur.  The  Compo- 
nents when  Fused  in  Conjunction  Unite  to  Form  One  or  More 
Chemical  Compounds  which  Melt  without  Decomposition. 

1.  GENERAL  CASE.  —  We  will  again  choose  two  elements  for 
the  components  of  our  system,  denoting  them,  as  well  as  their 
melting  points,  by  A  and  B.  For  simplicity,  we  will  assume 
only  one  compound,  possessing  the  formula  AmBn,  to  exist 
between  them.  In  this  formula,  m  and  n  are  simple  integers, 
according  to  the  law  of  multiple  proportions.  To  secure  better 
definition  at  the  start,  let  us  suppose  that  the  compound  con- 
tains 40  per  cent  A  and  60  per  cent  B.  We  assume  that  it  melts 
without  decomposition,  and  that  its  melting  point  is  C.  Our 
general  assumption  of  complete  miscibility  in  the  liquid  state  and 
complete  immiscibility  in  the  crystalline  state  applies  to  the  com- 
pound as  well  as  to  the  components. 

First  of  all,  let  us  confine  our  attention  to  that  part  of  the  con- 
centration-temperature diagram  which  is  located  between  0  and 
60  per  cent  B  (concentration  of  the  compound  AmBn).  In  view 
of  previous  explanations,  we  are  in  a  position  to  adequately 
define  the  general  character  of  this  part  of  the  fusion  diagram. 
In  effect,  we  have  a  two  component  system,  one  component 
being  A  and  the  other  B.  Under  our  primary  assumptions, 

1  A  thorough  thermal  and  microscopical  study  of  these  alloys  by  Gonter- 
mann,  published  about  a  month  after  this  book  left  the  hands  of  the  author, 
shows  conclusively  that  the  above  interpretation  is  correct.  Z.  anorg.  Chem., 
55,  419  (1907).  —  Translator. 


76 


THE  ELEMENTS  OF  METALLOGRAPHY. 


complete  miscibility  in  the  liquid  state,  and  complete  immisci- 
bility  in  the  crystalline  state,  obtain,  polymorphous  transforma- 
tions are  excluded,  and  the  two  components  give  no  compound 
with  each  other,  since  AmBn  is  the  only  compound  which  occurs. 
Thus,  we  are  dealing  with  the  very  case  discussed  under  A  (from 
p.  38).  Accordingly,  the  melting  point  of  A  will  be  lowered  by 
addition  of  AmBn,  and,  likewise,  the  melting  point  of  the  pure 
compound  fcy  addition  of  A.  Two  curve  branches  of  incomplete 
equilibrium,  AX  and  BY  (Fig.  16a),  are,  therefore,  to  be  expected, 


i  \ 


0      10      20      30      40      50 
Weight  per  Gent  B 
FIG.  16a. 


AmBn 


60    70      80      90     100 
AmBn  weight  per  cent  B 
FIG.  16b. 


each  of  them  maintaining  a  rectilinear  course  from  the  start,  as 
long  as  the  laws  of  dilute  solutions  hold.  The  crystalline  variety 
A  separates  along  AX,  the  variety  AmBn  along  AY.  The  two 
branches  intersect  at  the  eutectic  point  D.  An  eutectic  hori- 
zontal aDb  passes  through  this  point,  reaching,  on  the  one  hand, 
up  to  the  concentration  0  (pure  A),  and,  on  the  other  hand,  up 
to  the  concentration  60  (pure  compound  AmBn).  The  relative 
quantity  of  eutectic  is  at  its  maximum  value  1  at  the  concentra- 


TWO  COMPONENT  SYSTEMS.  77 

tion  D,  in  that,  here,  the  whole  alloy  crystallizes  eutectically,  and 
decreases  lineally  toward  both  sides,  reaching  the  zero  value 
at  concentrations  0  and  60,  respectively.  This  is  indicated  in 
the  usual  manner  by  erecting  verticals  on  the  concentration  axis, 
at  lengths  which  are  proportional  to  the  relative  quantities  of 
eutectic. 

We  may  also  consider  that  part  of  the  diagram  between  con- 
centrations 60  and  100  per  cent  B  separately,  in  like  manner 
(Fig.  16b).  The  melting  point  C  of  the  compound  AmBn  is 
lowered  by  addition  of  B,  and  that  of  B  by  addition  of  AmBn. 
We  have  here  a  system  composed  of  the  two  substances  B  and 
AmBn,  which  is  completely  analogous  to  the  preceding  system. 
Again,  we  observe  two  curve  branches,  namely,  CZ,  correspond- 
ing to  primary  separation  of  the  crystalline  variety  AmBn,  and 
BU,  corresponding  to  primary  separation  of  the  variety  J5,  which 
intersect  at  an  eutectic  point,  namely  E.  The  eutectic  horizontal 
cEd  passes  through  this  point  and  ends  at  concentration  60 
(pure  compound)  on  one  side,  and  at  concentration  100  (pure  B) 
on  the  other  side.  The  relative  quantity  of  eutectic  is  at  its 
maximum  value  at  the  eutectic  concentration  E,  and  decreases 
lineally  toward  both  sides,  reaching  the  zero  value  at  both  end 
points  of  the  eutectic  horizontal.  This  is  also  represented  in  the 
figure  (16b)  in  the  usual  manner. 

Now,  it  would  be  purely  a  matter  of  chance  if  the  temperature 
of  eutectic  crystallization  along  the  line  aDb  were  practically  the 
same  as  the  temperature  of  eutectic  crystallization  along  the  line 
cEd.  (We  use  the  words  practically  the  same,  since  the  possi- 
bility that  two  independent  processes  take  place  at  precisely  the 
same  temperature  may  be  disputed  on  the  basis  of  the  theory  of 
probabilities.)  In  general,  the  eutectic  horizontal  cEd  will  lie  at 
a  different  temperature  than  will  the  horizontal  aDb. 

At  this  point,  we  need  only  to  combine  the  two  single  diagrams 
into  one  (Fig.  16c)  in  order  to  obtain  the  general  form  of  fusion 
diagram  for  this  case.  The  following  trivial  modification  must  be 
observed  in  this  connection.  According  to  our  derivation,  the 
fusion  curve  ADCEB  is  composed  of  the  four  branches  AD,  CD, 
CE  and  BE,  all  running  rectilineally  at  the  start,  and  any  two 
successive  ones  intersecting  in  a  sharp  angle  (at  the  respective 
points  D,  C  and  E).  Such  a  trend  of  the  fusion  curve  in  the 


78 


THE  ELEMENTS  OF  METALLOGRAPHY. 


vicinity  of  C  (Fig.  16c)  is  indicated  by  dotted  branches.  In 
reality,  a  sharp  peak  never  occurs  at  C,  but,  rather,  a  more  or  less 
flattened  maximum,  as  shown  in  the  diagram  by  the  full  curve. 
Since  it  may  be  shown  theoretically1  that  an  upward  peak,  viz., 


0       10      20       30      40       50      60 
Weight  per  cent  B 

FIG.  16c. 


70      80      90     100 


a  point  elevated  above  its  immediate  surroundings,  can  never 
occur  upon  a  fusion  curve,  it  appears  that  whenever  the  experi- 
mental investigation  seems  to  indicate  the  presence  of  a  peak 
rather  than  a  maximum,  we  are,  in  fact,  dealing  with  a  maxi- 
mum, even  though  it  be  very  little  flattened. 

The  central  portion  DCE  of  the  fusion  curve  therefore  shows 
no  discontinuity  at  C  (it  manifests  no  abrupt  change  in  direction), 
and  is  to  be  regarded  as  a  single  curve  branch.  The  only  abrupt 
changes  in  direction  throughout  the  entire  course  of  the  curve 
are  at  D  and  E.  Accordingly,  there  are  only  three  branches, 
namely,  AD,  DCE  and  BE  (see  p.  50,  footnote). 

1  C/.  H.  A.  LORENTZ,  Z.  phys.  Chem.,  10,  194  (1892);  RUER,  Z.  phys. 
Chem.,  59,  1  (1907). 


TWO  COMPONENT  SYSTEMS.  79 

The  fact  that  a  maximum  instead  of  a  peak  appears  at  C  may  be 
regarded  as  a  consequence  of  the  partial  dissociation  of  the  compound, 
when  in  the  liquid  state,  into  its  components.  Assuming,  for  simplicity, 
that  the  formula  of  the  compound  is  AB,  the  dissociation  process  accom- 
panying fusion  is  represented  by  the  equation, 

AB  <=±A  +  B. 
The  massaction  law  yields  the  relation, 

[A][B]=k[AB], 

wherein  the  concentrations  of  the  several  varieties  of  molecules  are 
denoted  by  the  use  of  brackets.  As  soon  as  some  crystalline  AB  has 
separated,  i.e.,  as  soon  as  the  solution  has  become  saturated  with  AB, 
[AB]  becomes  constant  at  the  respective  temperature,  and  we  obtain, 

[A]  [B]  =  const. 

Addition  of  a,  foreign  substance  (we  grant  here  that  the  leading  assump- 
tions of  complete  miscibility  in  the  liquid  state  and  of  complete  immisci- 
bility  in  the  crystalline  state  —  which  have  applied  to  all  of  the  recent 
discussion  —  are  realized)  determines  a  lowering  of  the  melting  point  of 
AB,  and,  furthermore,  this  lowering  is  proportional  to  the  number  of  dis- 
solved molecules,  as  long  as  the  addition  is  so  slight  that  the  laws  of 
dilute  solutions  continue  to  hold.  Now,  the  actual  lowering  caused  by 
additions  of  A  and  B,  respectively,  is  lower  in  comparison.  For,  on 
increasing  the  quantity  of  A  in  the  melt,  a  decrease  in  the  quantity  of  B 
must  ensue,  owing  to  the  required  constancy  of  the  solubility  product 
[A]  [B],  i.e.,  a  certain  quantity  of  the  compound  AB  will  be  re-formed,  and 
thereby  free  A,  as  well  as  free  B,  utilized.  We  see,  then,  that  not  all  of 
the  added  quantity  of  A  operates  to  lower  the  melting  point,  but  only  a 
certain  percentage  allowance,  which,  for  unchanging  dissociation,  de- 
creases as  the  addition  of  A  is  made  smaller.  Obviously,  addition  of  B  to 
the  compound  AB  is  responsible  for  an  analogous  effect,  and  it  follows 
that  the  fusion  curve  in  the  vicinity  of  the  point  C  cannot  be  made  up 
of  two  straight  lines  intersecting  in  a  sharp  peak,  but  must,  on  the  con- 
trary, represent  a  more  or  less  flattened  maximum. 

If  the  dissociation  of  the  compound,  in  proximity  to  its  melting  point, 
is  very  slight,  only  a  trifling  portion  of  the  A  material,  or  B  material, 
respectively,  will  be  used  in  re-formation  of  the  compound,  and  the  fusion 
curve  at  C  will  approximately  represent  two  intersecting  straight  lines; 
at  all  events  it  will  show  a  well-marked  maximum  in  this  vicinity.  If, 
however,  the  dissociation  is  very  great,  in  which  case  the  solubility  prod- 
uct will  possess  a  high  value,  the  quantity  of  A  and  B,  which  serves  for 


80  THE  ELEMENTS  OF  METALLOGRAPHY. 

re-formation  of  the  compound,  and  is  therefore  unavailable  for  lower- 
ing the  melting  point  of  A B,  will  be  very  considerable,  particularly  at  the 
start.  That  is,  the  maximum  will  be  flat.  Both  cases  actually  occur, 
and  we  are  at  liberty  to  conclude  from  the  character  of  the  maximum  at 
C  whether  the  fused  compound  is  considerably,  or  only  slightly,  disso- 
ciated. In  accordance  with  the  above,  the  "true"  melting  points  of 
compounds  which  are  subject  to  such  dissociation  are  never  observed; 
lower  values  are  invariably  obtained. 

In  calculating  the  degree  of  dissociation  of  a  compound  from  the 
course  of  its  fusion  curve,  we  are  confronted  by  certain  difficulties.  In 
the  first  place,  the  change  in  value  of  the  solubility  product  with  the 
temperature  is  unknown,  and,  in  the  second  place,  a  compound  of  the 
general  formula  AmBn  may  dissociate  in  various  ways.  Thus,  the  com- 
pound AB2  may  dissociate  partially,  e.g.,  into  A  and  B2,  or  into  AB  and 
B}  as  well  as  completely  i.e.,  into  A  and  2B.  Nothing  whatever  is  known 
concerning  the  extent  to  which  these  various  dissociations  may  occur  in 
the  presence  of  one  another. 

According  to  the  above,  our  fusion  diagram  shows  the  follow- 
ing characteristics: 

(1)  The  fusion  curve  —  the  curve  of  incomplete  equilibrium 
joining  the  temperatures  of  initial  separation  of  a  crystalline 
variety  —  is  composed  of  the  three  branches  AD,  DCE  and  BE. 
A  definite  crystalline  variety  is  in  equilibrium  with  the  melt 
along  each  one  of  these  branches.  Along  the  branches  AD  and 
BE,  we  have  the  pure  substances  A  and  B,  respectively,  while, 
along  the  fusion  curve  DCE,  we  have  primary  separation  of 
the  compound  AmBn.  The  latter  is  especially  characterized  by 
its  capacity  for  existence  in  a  condition  of  equilibrium  with 
either  of  two  melts  of  different  concentration  at  one  and  the 
same  temperature.  By  way  of  illustration,  m  and  n  represent 
two  such  points  on  the  branch  DCE  —  they  are  equally  distant 
from  the  concentration  axis  and  therefore  correspond  to  the 
same  temperature.  In  this  connection,  we  will  regard  the  melt 
of  concentration  m  as  composed  of  molten  A,  saturated  with  the 
compound  AmBn  at  this  temperature,  and  the  melt  of  concentra- 
tion n  as  composed  of  molten  B,  likewise  saturated  with  the  com- 
pound at  this  temperature.  This  interpretation  is  confirmed  by 
the  fact  that,  in  the  first  case,  the  eutectic  is  made  up  of  the  two 
structure  elements  AmBn  and  A,  while,  in  the  second  case,  it  is 
made  up  of  AmBn  and  B.  (See  below.) 


TWO  COMPONENT  SYSTEMS.  81 

(2)  Of  the  three  branches,  one,  namely  DCE,  possesses  a  max- 
imum (at  C)  which  corresponds  to  the  compound  AmBn. 

(3)  At  length,   there   are  in  the   diagram  two   eutectic   hori- 
zontals, aDb  and  cEd,  corresponding  to  two  different  complete 
equilibria.     Along  the   horizontal   aDb,   we   find   the   crystalline 
varieties   A   and   AmBn   in   complete   equilibrium   with   melt   of 
invariable  composition  D.     Along  the  horizontal  cEd,  the  pre- 
vailing condition  of  complete  equilibrium  pertains  to  the  two 
crystalline  varieties  AmBn  and  B,  on  the  one  hand,  and  melt  of 
invariable  composition  E,  on  the  other  hand.     The  temperatures 
of  these  two  eutectic  horizontals  are  different.     The  relative  quan- 
tities of  eutectic  for  the  various  concentrations,  and  the  eutectic 
halting  periods  on  the  cooling  curves  which  are  proportional  to 
the  same  under  the  familiar  assumptions,  increase  lineally  along 
the  eutectic  horizontal  aDb  from  the  zero  value  at  concentration 
0  up  to  a  maximum  value  at  concentration   D,  and  thereupon 
decrease  lineally  to  a  second  zero  value  at  the  concentration  C  of 
the  compound.     Along  the  eutectic  horizontal  cEd,  an  analogous 
increase  from  zero  to  maximum  between  concentrations  C  and  E 
occurs,  as  well  as  an  analogous  decrease  from  maximum  to  zero 
between  concentrations  E  and  100. 

The  complete  concentration-temperature  diagram  is  divided  by 
the  curves  and  straight  lines  into  nine  fields  of  condition,  pro- 
vided we  consider  the  eutectics  as  individual  structure  elements, 
in  accordance  with  earlier  explanations.  Above  the  fusion  curve 
ADCEB,  all  alloys  exist  in  the  liquid  state;  we  have,  here,  the 
field  of  melt.  Between  the  fusion  curves  and  the  eutectic  hori- 
zontals, lie  the  fields  in  which  a  single  crystalline  variety  is  in 
equilibrium  with  melt.  Four  ''fields  with  one  crystalline  variety," 
as  we  shall  call  them,  are  in  evidence.  All  are  triangular  in  form, 
and  two  of  them  refer  to  the  compound  AmBn.  Their  character- 
ization follows: 

(1)  The  triangle  AaD.  In  this  field,  the  crystalline  variety  A 
occurs  in  equilibrium  with  melt.  Separation  of  A  takes  place 
along  the  curve  branch  AD.  During  this  process,  the  compo- 
sition of  the  melt  gradually  approaches  concentration  D.  The 
quantities  of  variety  A  and  melt,  into  which  any  given  mixture 
separated  on  attaining  a  position  in  this  field,  are  given  by  the 
lever  relation. 


82  THE  ELEMENTS  OF  METALLOGRAPHY. 

(2)  The  triangle  CbD.     This  is  a  field  of  the  crystalline  variety 
AmBn  and   melt.     On  falling  temperature,  separation  of  AmBn 
proceeds  along  the  branch  CD,  whereby  the  composition  of  the 
melt  continually  approaches  concentration  D. 

(3)  The  triangle  CcE.     This  is  also  characterized  as  a  field  of 
crystalline  variety  AmBn  and  melt.     In  fact,  we  have  already 
noted  that  the  compound  AmBn  may  exist  in  equilibrium  with 
two  different  melts  at  the  same  temperature.     On  falling  temper- 
ature,  crystallization  of    AmBn  proceeds  along  the  branch  CE, 
and  the  composition  of  the  melt  continually  approaches  concen- 
tration E. 

(4)  The   triangle   BdE.     This   is   the   field   of   the   crystalline 
variety  B  and  melt.     The  composition  of  the  latter  continually 
approaches  concentration  E  as  the  temperature  falls. 

The  four  fields  of  condition  in  which  the  alloys  are  entirely 
crystallized  are  situated  below  the  eutectic  horizontals  aDb  and 
cEd.  Since  two  crystalline  varieties  are  invariably  present  within 
these  fields,  we  denote  them  as  "fields  with  two  crystalline  varie- 
ties.'' Each  one  of  these  fields  is  subjoined  to  a  field  with  one 
crystalline  variety  (situated  directly  above  it).  (There  are  four 
of  each.)  Characterization  follows: 

(1)  The  field  with  two  crystalline  varieties  aDeh  corresponds 
to  the  superposed  field  with  one  crystalline  variety  A  Da.     After 
primary  separation  of  A  has  ceased,  the  residual  melt  will  have 
attained  the  composition  D,  and  will  henceforth  crystallize  at  the 
constant   temperature   of  the   eutectic   horizontal   aDb.     During 
this  time,   then,   we  find   ourselves  upon  the  limiting   line   aD 
which  belongs  to  neither  of  the  fields,  since  here  two  crystalline 
varieties  and  melt  are  in  equilibrium.     As  soon  as  the  whole  melt 
has  crystallized,  however,  we  cross  this  limiting   line  and  enter 
the  field  aDeh.     We  now  have  primarily  separated  A  crystals, 
surrounded  by  eutectic  of  concentration  D;  the  latter  composed 
of  the  two  crystalline  varieties  A  and  AmBn. 

(2)  The  field  with  two  crystalline  varieties  Dbfe  is  associated 
with  the  superposed  field  with   one   crystalline  variety  CbD  in 
exactly  the  same  manner.     In  this  case,  the  structure  elements 
are  primarily  separated  compound  AmBn,  surrounded  by  eutec- 
tic D;    the  latter  identical   with  the  eutectic  of   the  preceding 
field. 


TWO  COMPONENT  SYSTEMS.  83 

(3)  Primarily  separated  AmBn  is  also  present  in  the  field  with 
two  crystalline  varieties  Ecfg.     It  is,  however,  surrounded  by  a 
different  eutectic,  namely,  that  of  concentration  E,  composed  of 
the  two  crystalline  varieties  AmBn  and  B. 

(4)  Field    Edig   contains   the   primarily   separated    crystalline 
variety  5,  surrounded  by  eutectic  E;  the  latter  identical  with  the 
eutectic  of  field  3. 

In  accordance  with  the  above  detailed  characterization  of  the 
alloys  in  this  series,  we  shall  expect  the  following  results  on  micro- 
scopical examination  of  prepared  sections  of  the  corresponding 
reguli  : 

(1)  A  section  of  concentration  0  will  be  homogeneous,  showing 
the  single  crystalline  variety  A. 

(2)  Sections   of   concentrations   between   0   and   e   will   show 
primarily  separated  crystals  of  A,  surrounded  by  eutectic  D;  the 
latter  composed  of  the  two  varieties  A  and  AmBn.     The  quantity 
of  primarily  separated  crystals  will  decrease  with  increasing  con- 
centration, while  that  of  eutectic  will  increase. 

(3)  A  section  of  concentration  e  will  show  eutectic  D  alone;  no 
primarily  separated  single  crystalline  variety. 

(4)  Sections   of   concentrations   between   e   and  /  will    show 
primarily  separated   crystals  which   must  differ  from   those  in 
sections  1  and  2.      These  will  consist  of  compound  AmBn,  but 
the  surrounding  eutectic  will  be  identical  with  that  of  the  pre- 
ceding  sections.     The   quantity  of  AmBn  crystals  will  increase 
with    increasing   concentration,  while   that  of  eutectic  will  de- 
crease. 

(5)  A  section  of   concentration  /  =  C,  corresponding  in  com- 
position to  the  pure  compound,   can  show  only  one  crystalline 
variety,  namely  AmBn,  and  must  therefore  appear  completely 
homogeneous. 

(6)  Sections   of   concentrations    between  /  and   g   will    show 
the  same  primary  structure  element   as  did  sections  4   and   5, 
namely,  the  compound  AmBn.     However,  a  different  eutectic  E 
will  appear  here.     This  is  composed  of  the  two  crystalline  varie- 
ties AmBn  and  B.     The  quantity  of  primary  crystalline  variety 
will  decrease  with  increasing  concentration,  while  that  of  eutectic 
will  increase. 

The  new  eutectic  possesses  the  crystalline  variety  AmBn  in 


84  THE  ELEMENTS  OF  METALLOGRAPHY. 

common  with  the  previously  observed  eutectic,  but  contains  the 
variety  B  as  a  substitute  for  the  variety  A  of  the  latter.  There- 
fore, we  might  look  with  some  assurance  for  a  corresponding 
difference  in  the  appearance  of  the  two  eutectics.  Microscopical 
investigation  proves  inadequate,  however,  in  just  this  respect  — 
eutectics  of  different  composition  frequently  show  the  same  lam- 
ellar, or  finely  granular,  structure,  with  very  little  if  any  distinc- 
tion, while,  on  the  other  hand,  identical  eutectics  may  differ  more 
or  less  from  one  another  in  appearance  (cf.  p.  100).  The  tempera- 
ture at  which  an  eutectic  crystallizes  in  general  serves  as  the 
best  criterion  regarding  its  nature.  On  the  contrary,  the  presence 
of  eutectic  in  very  close  proximity  to  the  concentration  /  =  C  is 
usually  detected  to  better  effect  by  the  microscopical  method  than 
by  the  thermal  method. 

(7)  A  section  of  the  composition  g  will  show  eutectic  E  alone 
(same  condition  as  in  3). 

(8)  Sections  of  concentrations  between  g  and  i  (=  100  per  cent  B) 
will  show  a  new  crystalline  variety  B,  as  primary  structure  element, 
surrounded  by  the  same  eutectic  E  found  in  sections  6  and  7. 

(9)  A  section  of  concentration  100  contains  the  crystalline  variety 
B  only,  and  will  therefore  appear  completely  homogeneous. 

In  summation,  the  characteristic  properties  of  the  fusion 
diagram,  representing  the  mutual  behavior  of  two  substances 
according  to  the  assumptions  upon  which  our  discussion  has  been 
based,  are  as  follows: 

(1)  The  fusion  curve  is  made  up  of  three  branches,  of  which 
the  central  one  possesses  a  maximum. 

(2)  Two  different  temperatures  of  eutectic  crystallization  exist. 
One   eutectic  horizontal    begins  at   the  pure  substance  A]  the 
other  at  the  pure  substance  B.     Both  end  at  the  exact  concen- 
tration of  the  maximum  C  of  the  central  curve  branch. 

Conversely,  if  the  diagram  of  a  two  component  system  is  con- 
structed on  the  basis  of  cooling  curves  of  an  adequate  number  of 
different  concentrations  and  reveals  the  two  above  characteristics, 
we  are  at  liberty  to  conclude  that: 

(1)  Complete  miscibility  in  the  liquid  state  and  complete 
immiscibility  in  the  crystalline  state  obtain  (the  latter,  owing 
to  the  fact  that  both  eutectic  horizontals  begin  at  the  pure  sub- 
stances A  and  B,  respectively,  and  end  at  the  same  concentration). 


TWO  COMPONENT  SYSTEMS.  85 

(2)  The  two  components,  on  being  fused  in  conjunction,  unite 
to  form  a  single  chemical  compound  (subject,  of  course,  to  the 
limitations  discussed  on  p.  64). 

(3)  The  compound  fuses  without  decomposition. 

In  determining  the  composition  of  the  compound,  the  following 
expedients,1  based  upon  the  preceding  discussion,  are  brought 
into  requisition: 

(1)  The    composition    of   the    compound    corresponds    to    the 
maximum  C  of  the  central  branch  of  the  fusion  curve. 

(2)  The  eutectic  horizontal  aDb  ends  at  the  concentration  of 
the  pure  compound.     The  periods  of  eutectic  crystallization  are 
used,  in  the  familiar  manner,  in  locating  this  end  point.     Thus, 
when  verticals  are  erected  upon  the  concentration  axis  at  lengths 
which  are  proportional  to  the  eutectic  halting  points  on  the  cool- 
ing curves  (assuming  the  use  of  equal  quantities  of  substance  in 
all  experiments  as  well  as  equal  and  ideal  conditions  of  cooling), 
one  of  the  two  straight  lines  joining  the  end  points  of  these  verti- 
cals, namely  kf,  must  intersect  the  concentration  axis  at  the  con- 
centration /  of  the  pure  compound. 

(3)  The  same  (2)  holds  for  the  eutectic  horizontal  cEd,  in  that 
this  horizontal  also  ends  at  the  exact  concentration  of  the  com- 
pound —  the  straight  line  //  cuts  the  concentration  axis  at  the 
same  point/. 

These  three  criteria  check  one  another.  Two  other  criteria 
serve  by  way  of  further  confirmation: 

(4)  An  alloy  of  the  exact  concentration  of  the  compound  melts 
at  the  temperature  C  after  the  manner  of  a  pure  substance,  and 
should  show  no  eutectic  in  its  prepared  section. 

(5)  The  composition  of  the  compound  must  correspond  to  the 
law  of  multiple  proportions. 

Relative  to  the  value  of  the  individual  criteria,  we  may  say 
that  Criterion  1  may  be  depended  upon  for  accurate  results 
only  when  the  maximum  is  not  too  flat.  For,  even  though  the 
method  of  temperature  measurement  (discussion  of  such  methods 
follows  in  Part  II,  Practice)  be  admirably  developed,  differences 
of  some  5  degrees  between  individual  temperature  determinations, 
or  of  10  degrees  or  even  more  at  temperatures  above  1200  degrees, 
are  not  exceptional.  Unusual  care  in  experimentation  and  fre- 
1  TAMMANN,  Z.  anorg.  Chem.,  37,  303  (1903). 


86  THE  ELEMENTS  OF  METALLOGRAPHY. 

quent  repetition  of  the  separate  determinations  for  the  purpose  of 
securing  check  must  be  observed  if  any  considerable  reduction  of 
this  error  is  to  be  secured.  In  effect,  then,  if  the  maximum  is 
very  flat,  its  position  on  the  fusion  curve  is  often  uncertain  by 
several  per  cent,  particularly  in  cases  where  the  melt  is  disposed 
toward  supercooling,  viz.,  where  exact  determination  of  the 
initial  temperature  of  crystallization  is  subject  to  further  diffi- 
culty. In  dealing  with  what  appears  to  be  an  extremely  flat 
maximum,  there  may  be  considerable  doubt  as  to  whether  it 
actually  is  or  is  not  a  maximum.1 

Criteria  2  and  3  are  in  general  much  more  valuable,  as  first 
pointed  out  by  TAMMANN.  It  is  indeed  true  that  conditions  may 
operate  here  to  render  the  lines  hk,  fl  and  li,  joining  the  end 
points  of  the  verticals  which  represent  periods  of  eutectic  crys- 
tallization, curved  instead  of  straight.  We  note  particularly,  in 
this  connection,  the  effect  of  supercooling  and  the  impossibility  of 
completely  realizing  ideal  cooling  conditions  in  actual  practice. 
But,  on  the  one  hand,  these  two  sources  of  error  are  opposite  in 
effect,  and  compensate  one  another  in  many  cases,  as  will  be 
shown  later,  while,  on  the  other  hand,  when  the  lines  are  not 
straight,  but  are  curved  in  some  way,  their  prolongation  almost 
invariably  meets  the  concentration  axis  at  the  proper  locality. 
Moreover,  microscopic  examination  of  the  corresponding  sections 
usually  permits  very  accurate  estimation  of  the  concentrations 
at  which  the  eutectics  vanish. 

Criterion  4  is,  likewise,  of  especial  value  when  the  thermal 
investigation  is  confirmed  by  use  of  the  microscope  to  show 
that  the  solidified  alloy  in  question  is  actually  homogeneous,  con- 
taining no  eutectic,  or  at  most  a  negligible  trace  of  eutectic. 

Finally,  Criterion  5  is  of  little  value,  since  the  inter-metallic 
compounds  frequently  correspond  to  formulas  which,  in  the  first 
place,  are  rather  complicated,  and,  in  the  second  place,  fail  to 
conform  to  the  doctrine  of  valence  —  itself  a  development  based 
upon  the  investigation  of  compounds  between  metals  and  non- 
metals.  Thus,  ScHULLER2  describes  the  following  sodium-mer- 
cury compounds: 

NaHg4,  NaHg2,  Nal2Hg13,  NaHg,  Na3Hg2,  Na5Hg2,  and  Na3Hg. 

1  RUER,  Z.  anorg.  Chem.,  52,  350  (1907). 

2  SCHULLER,  Z.  anorg.  Chem.,  40,  385  (1904). 


TWO  COMPONENT  SYSTEMS. 


87 


At  this  point,  we  will  permit  the  limiting  assumption  that  the 
two  elements  form  only  one  compound  to  lapse.  We  will  con- 
tinue to  assume,  however,  that  each  compound  melts  without 
decomposition.  No  difficulty  will  be  met  in  handling  this  case, 
in  view  of  the  preceding  explanations.  Let  us  suppose  that  two, 
and  only  two,  compounds  exist.  The  two  components  of  the 


10   20   30   40  50   60  i  70   80   90  100 


Weight  per  cent  B 


! 
AoBp 


FIG.  17. 


system  and  their  melting  points  are  again  denoted  by  A  and  B. 
The  melting  point  of  one  compound  AmBn  is  C,  and  that  of  the 
other  compound,  of  composition  A0BP,  is  D.  If  the  whole  dia- 
gram (Fig.  17)  is  now  divided  into  three  parts  by  the  two  dotted 
lines  erected  upon  the  concentration  axis  at  the  respective  con- 
centrations of  the  two  compounds,  each  part  corresponds  to  a 
two  component  system  including  no  compound,  and  we  may 


88  THE  ELEMENTS  OF  METALLOGRAPHY. 

draw  the  same  conclusions  which  led  to  the  development  of  the 
fusion  diagram  including  a  single  compound. 

We  deduce  very  simply  that  the  fusion  curve  now  consists  of 
four  branches,  namely,  AE,  ECF,  FDG  and  GB.  The  two  cen- 
tral branches  each  possess  a  maximum  at  the  concentration  of 
the  respective  compound.  Furthermore,  we  have  the  three 
eutectic  horizontals  aEb,  cFd  and  eGf,  each  beginning  at  the  con- 
centration of  one  crystalline  variety  and  ending  at  that  of  the 
next.  The  temperatures  of  the  eutectical  horizontals  are  differ- 
ent. The  quantities  of  eutectic  at  the  several  concentrations  are 
indicated  in  the  usual  manner.  In  fixing  the  formulas  of  the  two 
compounds,  the  above-mentioned  expedients  are  brought  into 
requisition. 

We  see  that  a  particular  branch  of  the  fusion  curve  corresponds 
to  primary  separation  of  each  crystalline  variety.  These  por- 
tions of  the  fusion  curve  have  been  termed  branches  because  they 
are  separated  from  one  another  by  points  (E,  F,  G)  where  an 
abrupt  change  in  direction  of  the  curve  occurs.  If,  as  in  the 
current  case,  two  compounds  are  existent,  there  are  four  separate 
crystalline  varieties  (including  the  two  pure  components)  and  also 
four  branches  of  the  curve.  Thus,  we  may  affirm  for  such  cases, 
under  the  assumption  that  only  one  crystalline  variety  corre- 
sponds to  each  substance,  that  the  number  of  compounds  V  is 
equal  to  the  number  of  branches  of  the  fusion  curve  A  less  2: 

V  =  A  -  2. 

Nevertheless,  this  relation  is  by  no  means  a  generality.  It  does 
not  of  necessity  hold  when  one  of  the  substances  appears  in  two 
crystalline  modifications,  viz.,  when  polymorphous  transforma- 
tions occur.  Again,  it  requires  that  the  assumption,  "  complete 
miscibility  in  the  liquid  state,  complete  immiscibility  in  the 
crystalline  state,"  be  realized.  Even  in  these  cases,  this  rule  is 
frequently  of  no  practical  importance,  since  a  branch  of  the  fusion 
curve  may  be  dwarfed  beyond  recognition  (see  Fig.  14,  p.  71),  or 
abrupt  changes  in  direction  along  the  curve  may  be  imperceptible. 

Since  precisely  two  crystalline  varieties  are  required  in  the 
formation  of  an  eutectic,  the  following  analogous  rule  may  be 
composed:  The  number  of  compounds  V  is  equal  to  the  number 


TWO  COMPONENT  SYSTEMS. 


89 


of  eutectic  horizontals  E  less  1,  under  the  assumption  that  no 
polymorphous  transformations  occur: 

V  =  E  -  1. 

The  validity  of  this  rule  is  dependent  upon  the  same  assump- 
tions, in  general,  as  that  of  the  first  rule,  and,  in  addition,  upon  an 
extension  of  our  conception  of  an  eutectic  horizontal  on  the  basis 
of  criteria  which  presume  very  exact  knowledge  of  the  complete 
fusion  diagram. 

All  such  rules  are  of  interest  merely  in  the  sense  that  they  may 
serve  the  purposes  of  a  preliminary  survey.  Knowledge  of  the 
complete  fusion  diagram  is  essential  in  formulating  final  answers 
to  questions  as  to  what  and  how  many  compounds  are  formed 
between  two  substances. 

2.  MAGNESIUM-TIN  ALLOYS.  —  We  will  now  proceed  to  the  dis- 
cussion of  examples  under  the  above  general  case,  first  directing 
attention  to  the  fusion  diagram  of  the  magnesium-tin  alloys,  as 
constructed  by  GRUBE.'  His  summary  of  results  obtained  from 
cooling  curves  is  given  in  Table  2. 

TABLE  2. 


Weight 
per  cent 
tin. 

Weight 
per  cent 
magne- 
sium. 

Atomic 
per  cent 
tin. 

Atomic 
per  cent 
magne- 
sium. 

Temp,  of 
breaks. 

Temp,  of 
eutectic  halt- 
ing points. 

Duration  of 
eutectic  crys- 
tallization in 
seconds. 

0 

100.00 

0 

100.00 

M.P.  650.9°.  Time  of  crystalliza- 

tion 125 

10.00 

90.00 

2.22 

97.78 

625.0° 

565.0° 

15 

20.00 

80.00 

4.87 

95.13 

607.5 

566.1 

40 

30.00 

70.00 

8.07 

91.93 

583.0 

564.6 

85 

40.00 

60.00 

12.01 

87.99 

585.4 

565.1 

140 

50.00 

50.00 

16.99 

83.01 

698.0 

566.3 

75 

60.00 

40.00 

23.46 

76.54 

753.5 

564.8 

35 

65.00 

35.00 

27.55 

72.45 

773.7 

561.9 

20 

70.95 

29.05 

33.33 

66.67 

Separation   of  compound   SnMg2 
at   783.4°.  Time  of  crystalliza- 

tion 110 

75.00 

25.00 

38.05 

61.95 

754.1 

204.5 

40 

80.00 

20.00 

44.55 

55.45 

720.0 

211.2 

90 

85.00 

15.00 

53.70 

46.30 

666.1 

210.3 

145 

90.00 

10.00 

64.82 

35.18 

550.0 

210.3 

200 

95.00 

5.00 

79.55 

20.45 

330.5 

210.5 

240 

97.50 

2.50 

88.87 

11.13 

217.4 

209.3 

275 

99.00 

1.00 

95.29 

4.71 

220.0 

209.4 

125 

100.00 

0 

100.00 

0 

M.P.  231.5°.  Time  of  crystalliza- 

tion 250 

1  GRUBE,  Z.  anorg.  Chem.,  46,  76  (1905). 


90  THE  ELEMENTS  OF  METALLOGRAPHY. 

We  find  in  this  table: 

(1)  The  composition  of  such  melts  as  were  investigated,  in  both 
weight  and  atomic  per  cent. 

(2)  The   temperatures   at   which   primary   separation   of   each 
crystalline   variety   begins.     Since   these   temperatures   are   ren- 
dered perceptible  upon  the  cooling  curves  by  abrupt  changes  in 
direction,  or  breaks,  they  are  entered  as  "breaks"  in  the  table. 

(3)  The  temperatures  of  eutectic  halting  points. 

(4)  The    periods    of    duration    of    eutectic    crystallization,    in 
which  connection  all  cooling  experiments  were  conducted  with 
the  same  total  quantity  of  material   (20  grams),  and  under  as 
uniform  conditions  as  were  possible. 

The  breaks  and  halting  points  tabulated  above  are  entered  by 
the  author  in  a  co-ordinate  system;  concentrations  appearing  as 
abscissas,  and  temperatures  as  ordinates,  in  the  well-known 
manner.  Observed  points  are  denoted  by  crosses.  The  con- 
centration axis  is  graduated  in  weight  per  cent  tin,  from  10  to  10 
per  cent  progressively.  Thus,  concentration  0  corresponds  to 
pure  magnesium,  and  concentration  100,  to  pure  tin.  The 
atomic  per  cents  which  correspond  to  these  even  decimal  weight 
per  cent  units  are  entered  upon  a  horizontal  line  immediately 
above  the  concentration  axis.  This  diagram  is  reproduced  in 
Fig.  18. 

The  fusion  curve,  or  the  curve  giving  the  temperature  of  pri- 
mary separation  of  one  crystalline  variety  throughout  the  series, 
is  made  up  of  the  three  branches  AB,  BCD  and  DE.  The 
branches  AB  and  DE  are  approximately  rectilinear,  while  the 
branch  BCD  possesses  a  well-marked  maximum  situated  at 
the  temperature  783.4  degrees  (see  Table).  The  branches  BCD 
and  DE  intersect  at  the  eutectic  point  D  —  concentration  97.5 
weight  per  cent  tin  —  while  the  branches  BCD  and  AB  intersect  at 
the  eutectic  point  B  —  concentration  38.7  weight  per  cent  tin. 
The  mean  value  for  the  eutectic  temperature  B,  calculated  from 
the  several  observed  values  given  in  the  table,  is  564.8  degrees, 
and  for  the  eutectic  temperature  D,  209.4  degrees.  Thus,  the 
temperature  difference  between  the  two  eutectic  horizontals 
amounts  to  some  350  degrees.  The  first  eutectic  horizontal  com- 
mences at  pure  magnesium  and  ends  at  the  point  c,  located 
very  nearly  upon  the  vertical  which  bears  the  maximum  C.  The 


TWO  COMPONENT  SYSTEMS. 


91 


800 


750° 


650° 


550° 


450° 


350° 


250° 


150 


50 


2.22       4.87        8.07      12.01       16.99      23.46     32.30       44.55     64.82       1( 
Atomic  per  cent  Tin 


10  20  30  40  50  60  70 

Weight  per  cent  Tin 


90         100  Sn 


FIG.  18.     Fusion  Diagram  of  Magnesium-Tin  Alloys  according  to  Grube. 


92  THE  ELEMENTS  OF  METALLOGRAPHY. 

second  eutectic  horizontal  extends  from  this  exact  concentration 
(C)'to  pure  tin.  (Concerning  the  method  of  ascertaining  these 
end  points,  see  subsequent  discussion.) 

It  is  quite  evident  that  this  diagram  by  Grube,  based  upon  his 
experimental  cooling  curves,  possesses  the  exact  characteristics 
of  the  diagram  which  we  have  developed  to  cover  the  general 
case  requiring  that  two  substances,  on  being  fused  in  conjunction, 
form  a  single  chemical  compound  melting  without  decompo- 
sition, there  being  complete  miscibility  throughout  the  liquid 
phase,  complete  immiscibility  between  the  solid  phases,  and 
entire  absence  of  polymorphous  transformation. 

The  composition  of  the  compound  in  question  corresponds  to 
the  formula  SnMg2,  requiring  70.95  weight  per  cent  tin  and  29.05 
weight  per  cent  magnesium. 

Grube  resorted  to  the  previously  mentioned  (p.  85)  expedients 
in  determining  the  composition  of  the  compound.  He  specifies 
the  following  in  this  connection: 

(1)  By  graphical  interpolation,  the  maximum  C  of  the  fusion 
curve  (constructed  from  experimental  data)  is  found  to  possess  a 
concentration  value  between  70.5  and  71.5  weight  per  cent  tin. 

(2)  The  end  points  of  the  two  eutectic  horizontals  are  found 
to  lie  at  70.8  weight  per  cent  tin,  and  71  per  cent  tin,  respec- 
tively. 

We  are  aware  that,  provided  there  is  no  miscibility  in  the 
crystalline  state,  both  eutectic  horizontals  must  end  at  the 
concentration  of  the  compound.  Thus  far,  the  eutectic  periods 
of  crystallization  have  been  represented  graphically  by  erecting 
verticals  upon  the  concentration  axis  at  the  respective  concentra- 
tions, and  at  lengths  proportional  to  these  respective  periods. 
Grube  uses  the  eutectic  horizontals  themselves  as  base  lines  for 
construction  of  these  verticals  in  the  reverse  direction  (downward). 
This  trifling  alteration  is  very  practical  in  complicated  cases 
where  several  horizontals  frequently  interfere  with  one  another 
part  of  the  way,  since,  when  this  method  is  adopted,  the  applica- 
tion of  the  verticals  to  their  respective  horizontals  is  at  once 
apparent.  We  see  that  the  decrease  from  6  to  a  and  from  6  to  c 
below  the  horizontal  aBc  is  by  no  means  linear.  In  discussing  the 
general  case,  we  referred  to  the  frequent  occurrence  of  such  anom- 
alies in  the  fusion  diagram  and  to  their  forthcoming  explanation 


TWO  COMPONENT  SYSTEMS.  93 

(in  Part  II).  It  is,  however,  evident  that  prolongation  of  the  curve 
joining  the  end  points  of  the  verticals  results  in  its  intersection 
with  the  eutectic  horizontal  at  the  point  a  of  concentration  0  (at 
pure  magnesium),  on  the  one  hand,  and  at  the  point  c  of  concen- 
tration 70.8  on  the  other  hand.  The  eutectic  periods  decrease 
lineally,  within  the  limits  of  observation,  along  the  eutectic  hori- 
zontal dDf.  The  lines  joining  the  end  points  of  these  verticals 
are  therefore  straight,  and  we  have  for  points  of  intersection  with 
the  ground  line  (horizontal),/  of  concentration  100  (pure  tin),  on 
the  one  hand,  and  d  of  concentration  71,  on  the  other  hand. 

In  summation,  then,  the  values  for  the  composition  of  the 
compound,  70.8  per  cent  Sn  and  71  per  cent  Sn,  obtained  with 
the  aid  of  the  eutectic  periods,  agree  excellently  with  one  another, 
and,  within  the  limits  of  experimental  error,  with  the  concentra- 
tion value  found  for  the  maximum  of  the  fusion  curve,  namely, 
70.5  —  71.5  per  cent  Sn. 

By  way  of  further  check,  Grube  took  the  cooling  curve  of  an 
alloy  corresponding  exactly  to  the  compound  SnMg2  in  compo- 
sition (containing  70.95  per  cent  Sn).  This  cooling  curve  was 
that  of  a  pure  substance,  showing  a  halting  point  at  which  the 
temperature  remained  constant  during  along  period  of  time  (110 
seconds).  This  halting  point  appeared  at  a  higher  temperature 
(783.4  degrees)  than  did  the  breaks  upon  cooling  curves  of 
neighboring  concentrations  (65  and  75  per  cent  Sn),  and,  hence, 
must  actually  correspond  to  a  maximum  (cf.  Table  2).  Ac- 
cordingly, the  melting  point  of  the  compound  lies  at  783.4 
degrees.  The  melting  point  of  the  compound  is  considerably 
above  the  melting  point  of  the  less  fusible  component;  a  condi- 
tion which  is  frequently  realized.  Grube  makes  no  mention  of 
having  proved  the  unity  of  the  alloy  of  the  above  concentra- 
tion and  the  absence  of  an  eutectic  structure  element  by 
microscopical  investigation.  Presumably,  the  brittleness  of  the 
pure  compound,  which  he  mentions,  precluded  preparation  of  a 
serviceable  section. 

Finally,  the  simplicity  of  the  above  formula,  added  to  the  cir- 
cumstance that  it  satisfies  the  requirements  of  the  valence 
theory,  may  be  regarded  as  further  confirmation  of  the  con- 
clusions which  have  been  drawn  from  the  diagram. 

The  fields  of  condition  of  the  diagram  are  as  follows:    Above 


94 


THE  ELEMENTS  OF  METALLOGRAPHY. 


the  fusion  curve  ABODE,  the  alloys  of  all  concentrations  are 
entirely  liquid.  In  the  three-cornered  fields,  bounded  above  by 
the  fusion  curve  and  below  by  the  eutectic  horizontals,  we  have 
one  respective  crystalline  variety  in  equilibrium  with  melt. 
Below  the  eutectic  horizontals,  the  alloys  of  all  concentrations 
are  entirely  solid,  and  are  invariably  made  up  of  two  crystalline 
varieties.  Table  3  gives  a  summary  of  the  fields. 

TABLE  3. 

Fields  of  condition 


with  one  crystalline 
variety. 


with  two  crystalline  varieties. 


ABa 
CBc 
DCd 
DEf 

Mg 

SnMg2 
SnMg2 
Sn 

aBhg 
Bcih 
Dkid 
Dflk 

Mg  +  Eutectic  B  [Mg  +  SnMg2] 
SnMg2  +  Eutectic  B  [Mg  +  SnMg2] 
SnMg2  +  Eutectic  D  [Sn  +  SnMg2] 
Sn  +  Eutectic  D  [Sn  +  SnMg2] 

The  branch  AB  of  the  fusion  curve  appears  much  more  de- 
veloped in  the  diagram  than  does  the  branch  ED.  This  is, 
however,  due  to  the  use  of  weight  per  cents  in  graduating  the  con- 
centration axis.  If  concentrations  are  expressed  in  atomic  per 
cent,  the  point  B  becomes  located  at  11.60  atomic  per  cent  tin, 
and  the  point  D  at  11.13  atomic  per  cent  magnesium,  values 
which  merely  chance  to  virtually  coincide. 

KURNAKOW  and  STEPANOW  l  have  also  investigated  this  alloy 
series.  Their  results  agree  with  those  of  Grube  in  all  essential 
points,  and  their  fusion  diagram  need  not  be  reviewed  here. 
Nevertheless,  we  propose  to  devote  some  attention  to  their  micro- 
photographs  because,  in  the  first  place,  they  have  been  prepared 
with  great  care  and,  owing  to  marked  differences  between  the 
properties  of  compound  and  components,  show  the  structure 
unusually  well,  and  then  again,  because  comparison  of  the 
evidence  from  the  fusion  diagram,  which  is  particularly  clear  in 
this  instance,  with  the  conclusions  to  be  drawn  from  structural 
relations  of  the  sections,  which  are  in  turn  unusually  pictorial  in 
this  case,  is  well  adapted  to  show  how  far  both  methods  of  inves- 
tigation support  and  ultimately  elaborate  one  another. 

1  KURNAKOW  and  STEPANOW,  Z.  anorg.  Chem.,  46,  177  (1905). 


TWO  COMPONENT  SYSTEMS.  95 

We  may  say,  relative  to  the  properties  of  the  three  crystalline 
varieties,  that  the  compound  Mg2Sn  shows  octahedral  cleavage, 
and  that  its  hardness  (  =  3.5)  is  considerably  greater  than  that 
of  either  pure  component.  (Tin  =1.8,  magnesium  =  2.)  Fur- 
thermore, the  solidified  alloys  oxidize  in  damp  air  at  a  rate  which 
increases  with  their  magnesium  content. 

The  sections  shown  in  Figs.  19,  20  and  21  represent  alloys  con- 
taining from  10  to  30  per  cent  tin,  and  therefore  fall  within  the 
field  with  two  crystalline  varieties  a'Bhg  (Fig.  18).  Primary 
separation  of  magnesium  has  followed  the  curve  branch  AB. 


FIG.  19.    10%  Sn,  magnified  70  times. 

The  reguli  were  first  ground  and  then  polished  by  means  of  very 
finely  ground  emery,  placed  wet  upon  a  metal  plate  covered  with 
chamois.  The  dampness  of  the  leather  pad  brought  about  com- 
plete surface  oxidation  of  the  sections.  After  being  etched  in 
this  manner,  the  sections  were  rubbed  down  on  dry  chamois, 
covered  with  finely  ground  "saflor"  (cobalt  glance).  As  a  result 
of  this  process,  the  harder  constituent,  namely,  the  compound, 
SnMg2,  which  was  least  worn  away  by  rubbing,  and  therefore 
remained  somewhat  in  relief,  lost  its  coating  of  oxide  and  became 
brilliant,  while  the  metallic  magnesium  remained  dark.  Fig.  19 
represents  a  section  containing  10  per  cent  tin,  magnified  70  times. 
It  consists,  for  the  most  part,  of  grains  of  magnesium.  Enclosed 


96         THE  ELEMENTS  OF  METALLOGRAPHY. 


FIG.  20.    24%  Sn,  magnified  100  times. 


FIG.  21.    30%  Sn,  magnified  100  times. 


TWO  COMPONENT  SYSTEMS. 


97 


within  the  mass  of  these  grains,  we  find  appreciable  quantities  of 
light  eutectic,  which  permeates  the  predominant  material  in  the 
form  of  thin  veins.  In  Fig.  20,  which  represents  a  section  con- 
taining 24  per  cent  tin,  magnified  100  times,  dark  dendrites  of 
primarily  separated  magnesium  are  visible.  The  interstices  are 
filled  with  beautifully  developed  eutectic,  composed  of  alternate 
layers  of  darkly  etched  magnesium  and  light  compound  SnMg2. 
We  may  roughly  estimate  the  relative  quantity  of  eutectic  at  one- 
half  by  volume.  Fig.  21,  corresponding  to  30  per  cent  tin,  pre- 
sents essentially  the  same  picture;  there  is  merely  a  decrease  in 


FIG.  22.    39%  Sn,  magnified  170  times. 

the  relative  quantity  of  primarily  separated  magnesium,  and,  con- 
versely, an  increase  in  the  relative  quantity  of  eutectic,  as  re- 
quired by  the  diagram. 

Fig.  22  corresponds  to  39  per  cent  tin  (concentration  B  in  the 
diagram).  It  must,  therefore,  show  nothing  but  eutectic.  This 
section  was  prepared  in  the  same  manner  as  were  sections  19,  20 
and  21.  The  typical  lame/liar  eutectic  structure  —  called  typical 
on  account  of  its  general  occurrence  —  appears  here,  under  the 
chosen  magnification  of  170  times,  with  a  sharpness  and  distinct- 
ness which  is  seldom  attained  in  practice. 

Figs.  23-27  correspond  to  concentrations  from  42  to  62  per  cent 
tin,  and  accordingly  belong  in  the  field  of  two  crystalline  varieties 


98 


THE  ELEMENTS  OF  METALLOGRAPHY. 


FIG.  23.    42%  Sn,  magnified  70  times. 


FIG.  24.    46%  Sn,  magnified  70  times. 


TWO  COMPONENT  SYSTEMS. 


99 


FIG.  25.    50%  Sn,  magnified  70  times. 


FIG.  26.    56%  Sn,  magnified  60  times. 


100  THE  ELEMENTS  OF  METALLOGRAPHY. 

Bcih.  A  glance  at  the  diagram  informs  us  that,  in  these  concen- 
trations, a  new  crystalline  variety,  namely,  the  compound  SnMg2, 
separates  along  the  curve  branch  CB,  but  that  the  eutectic,  crys- 
tallizing last,  must  be  the  same  as  in  the  former  sections.  No  change 
was  made  in  the  preparation  of  the  sections.  We  at  once  recog- 
nize the  difference  between  the  primary  structure  element  of  these 
sections,  and  that  of  the  sections  previously  considered.  The  light 
sharp-edged  crystals  of  the  compound  SnMg2,  often  elongated  in 
one  direction,  cannot  be  confused  with  the  rounded  grains,  or 


FIG.  27.    62%  Sn,  magnified  70  times. 

dentrites,  of  magnesium,  coated  with  a  dark  layer  of  oxide.  We 
also  recognize  conformity  with  the  diagrammatic  evidence,  in 
the  sense  that  the  quantity  of  primarily  separated  crystals  in- 
creases with  the  tin-content  of  the  alloys,  while  the  quantity  of 
eutectic  simultaneously  decreases.  The  structure  of  the  eutectic, 
however,  is  not  as  clear  in  these  photographs  as  it  was  in  Figs. 
20-22.  We  could  scarcely  affirm,  on  the  basis  of  the  microscopic 
examination  alone,  that  this  eutectic  is  identical  with  the  one 
observed  in  the  former  sections.  In  reaching  this  conclusion,  we 
must  make  use  of  the  unambiguous  diagrammatic  evidence  which, 
although  unsupported  in  this  special  case  by  the  appearance  of 
the  eutectic,  is  not  contradicted  by  the  same. 


TWO  COMPONENT  SYSTEMS.  101 

Figs.  28  and  29  represent  sections  containing  83  and  91  per 
cent  tin,  respectively,  and  therefore  belong  to  the  field  with  two 
crystalline  varieties  Dkid.  Primary  separation  of  the  compound 
has  here  occurred  along  the  branch  CD.  Hence,  we  must  observe 
the  same  primary  crystalline  variety,  namely  the  compound 
SnMg2,  as  in  sections  23-27.  However,  in  these  sections  the 
second  eutectic  appears.  This  is  composed  of  the  compound 
SnMg2  and  pure  tin  (in  the  place  of  magnesium).  Moreover,  a 
simple  calculation  based  upon  the  composition  of  this  eutectic, 


FIG.  28.    83%  Sn,  magnified  40  times. 

as  given  in  the  diagram,  and  use  of  the  lever  relation  shows  us 
that  it  contains  more  than  90  per  cent  tin. 

The  preparation  of  these  sections  was  somewhat  different  from 
that  of  the  former  sections.  It  was  limited  to  simple  grinding, 
followed  by  polishing  on  the  leather-covered  metal  plate,  with 
use  of  fine  emery.  This  process  causes  oxidation  of  the  com- 
pound SnMg2  only;  the  tin  remaining  unchanged.  Subsequent 
rubbing  down  was  omitted.  The  dark  appearance  of  the  pri- 
marily separated  compound  SnMg2  find  its  explanation  in  this 
altered  method  of  preparation.  As  is  well  represented  in  Fig.  29, 
the  contour  of  these  primary  crystals  is  apparently  the  same  as 
that  shown  in  the  preceding  pictures.  The  eutectic  has  remained 
almost  completely  bright  and,  in  accordance  with  its  composition 


102 


THE  ELEMENTS  OF  METALLOGRAPHY. 


FJG.  29.    91%  Sn,  magnified  45  times. 


FIG.  30.    99%  Sn,  magnified  50  times. 


TWO  COMPONENT  SYSTEMS.  103 

as  noted  above,  shows  only  small  quantities  of  the  compound 
SnMg2  in  the  form  of  small  dark  evenly  distributed  crystals.  As 
the  tin-content  increases,  the  quantity  of  eutectic  increases  and 
that  of  primary  crystals  decreases,  in  line  with  the  requirements 
of  the  diagram.  It  is  also  plainly  evident  that  this  bright  eutectic 
is  different  from  the  eutectic  of  the  first  sections  (composed  of 
approximately  equal  parts  of  magnesium  and  compound).  In- 
deed, wet  polishing  of  sections  19-27  caused  simultaneous  oxida- 
tion of  both  structure  elements,  so  that  subsequent  dry  polishing 
on  rouge  was  necessary  in  order  to  give  the  compound  a  bright 
appearance.  Since  the  latter  step  was  not  observed  in  the 
treatment  of  sections  28  and  29,  the  eutectic  which  they  contain 
would  of  necessity  have  presented  a  dark  appearance  if  it  had 
been  identical  with  that  of  the  first  sections. 

Fig.  30  shows  a  section  containing  99  per  cent  tin,  viz.,  one 
falling  within  the  field  Dflk,  magnified  50  times.  The  diagram 
informs  us  that  a  new  crystalline  variety,  namely  pure  tin,  has 
separated  primarily  along  the  curve  branch  ED.  The  eutectic 
does  not  differ  from  that  shown  in  the  two  preceding  pictures. 
This  photograph  is  taken  from  Grube's  paper;  his  use  of  a  different 
etching  agent  precludes  comparison  of  this  section  with  preced- 
ing ones.  However,  we  note  the  presence  of  a  liberal  quantity  of 
a  bright  eutectic,  forming  a  matrix  in  which  dark  crystals  of  tin 
are  imbedded. 

We  have  seen  above  that  the  diagrammatic  evidence  is  cor- 
roborated by  the  appearance  of  the  sections,  as  far  as  they  present 
characteristic  structure,  and  that  no  contradiction  is  to  be  noted. 
As  a  result,  the  general  conclusions  must  be  accredited  with  a 
high  degree  of  certainty. 

3.  MAGNESIUM-BISMUTH  ALLOYS.  —  The  fusion  diagram  of  the 
System  Magnesium-Bismuth  has  also  been  studied  by  GRUBE.* 
His  experimental  results  are  summarized  in  Table  4,  and  his  dia- 
gram is  reproduced  in  Fig.  31.  Observed  points  are  denoted  by 
crosses.  We  note  the  occurrence  of  complete  miscibility  in  the 
liquid  state,  the  entire  absence  of  miscibility  in  the  crystalline 
state,  the  absence  of  polymorphous  transformation,  and  that 
the  two  metals  unite  to  form  one  compound  —  of  formula 
Bi2Mg,. 

1  GRUBE,  Z.  anorg.  Chem.,  49,  83  (1906) 


104 


THE  ELEMENTS  OF  METALLOGRAPHY. 


This  diagram  serves  to  illustrate  the  earlier  mentioned  possi- 
bility (Fig.  14,  p.  71;  p.  88)  that  a  branch  of  the  fusion  curve  be 
so  dwarfed  as  to  practically  disappear.  This  is  observed  on  the 
side  of  pure  bismuth,  the  melting  point  of  which  is  immediately 
elevated  along  the  curve  branch  DC  by  addition  of  magnesium. 
The  temperature  of  the  eutectic  horizontal  DC  (268  degrees) 
practically  coincides  with  the  melting  temperature  of  pure  bis- 
muth (268  degrees).  Again,  the  compound  Bi2Mg3  invariably 
separates  primarily  from  bismuth-rich  melts,  never  pure  bis- 
muth. Accordingly,  the  eutectic  must  be  composed  of  a  single 
crystalline  variety,  namely,  pure  bismuth. 

TABLE  4. 


Bismuth-content  of 
the  alloys. 

Temp,  of 
breaks. 

Temp,  of 
eutectic  halt- 
ing points. 

Duration  of 
eutectic  crys- 
tallization in 
seconds. 

Supercooling 
during  eutectic 
crystallization. 

Wt.  per 
cent. 

At.  per 
cent. 

0 
10.00 
20.00 
30.00 
40.00 
50.00 
60.00 
70.00 
80.00 
82.50 
83.50 
85.09 

87.50 
90.00 
95.00 
97.50 
100.00 

0 
1.28 
2.84 
4.77 
7.39 
10.46 
14.46 
21.42 
31.85 
35.51 
37.16 
40.00 

44.98 
51.26 
68.92 
81.97 
100.00 

M.P.  of  pur 
640 
626 
623 
604 
583 
564 
610 
677 
698 
710 
M.P.  of  the 

699 
612 
527 
432 
M.P.  of  pu 

e  Mg  650.9°. 
552 
553 
552 
554 
551 
553 
551 
552 
550 

Time  of  cry 
5 
20 
40 
60 
80 
95 
75 
30 
15 

stallization  125 

pure  c'p'd  Bi 
lizat 
269 
268 
268 
268 
re  Bi  268°.    r 

2Mg3715°.    T 
on  72 
55 
120 
150 
230 
Time  of  cryst 

ime  of  crystal- 

2 
4 

8 
7 
allization  250 

The  maximum  C  of  the  fusion  curve  at  the  concentration  of 
the  compound  appears  to  be  unusually  sharp;  in  fact,  there  is 
practically  no  distinction  between  this  maximum  and  a  sharp 
peak.  On  this  basis,  we  might  be  led  to  conclude  that  the  com- 
pound Bi2Mg3  is  practically  undissociated  in  the  molten  condition 
at  its  melting  temperature  (cf.  p.  79).  When,  however,  we 
graduate  the  concentration  axis  in  atomic  per  cent,  instead  of 


TWO  COMPONENT  SYSTEMS. 


105 


Melt 


Melt 


+B 


Melt 


\f\ 


Atomic  per  cent  Bismuth 


\e 


1.28       2. 


34      4. 


59      10 


46     14 


46    21 


42     31 


85    51 


26    10( 


Weight  per  cent  Bismuth 


10         20         30         40         50         60         70         30         90       100 
FIG.  31.     Fusion  Diagram  of  Magnesium-Bismuth  Alloys  according  to  Grube. 


106 


THE  ELEMENTS  OF  METALLOGRAPHY. 


weight  per  cent,  the  fusion  curve  shows  a  maximum  of  the  usual 
form  at  the  concentration  of  the  compound.  A  glance  at  the 
diagram  shown  in  Fig.  32  will  serve  to  make  this  clear.  This 


800' 


700° 
A 

600° 
500° 
400° 
300° 

200° 
Ma 

C 
£ 

s. 

\ 

/ 

\ 

X 

a    JV/ 

B 

0 

\ 

s, 

_3j 

\y 

\ 

\ 
\ 

V 

/ 

\ 

\ 

\ 

\ 

c 

\ 

^ 

'-^^ 

«^. 

~-^_ 

10      20       30      40      50      60       70      80      90     100 
Atomic  per  cent  Bismuth 

FIG.  32.     Fusion  Diagram  of  Magnesium-Bismuth  Alloys. 

latter  diagram  is  drawn  from  the  data  given  in  Grube's  table, 
and  differs  from  that  shown  in  Fig.  31  chiefly  in  that  the  concen- 
tration axis  shows  atomic  per  cents  in  units  of  10.  The  points 
which  were  directly  ascertained  by  experiment  are  again  denoted 
by  crosses.  The  method  of  representation  chosen  by  Grube 
brings  about  a  certain  distortion  of  the  fusion  curve,  owing  to 
the  great  difference  in  the  atomic  weights  of  the  two  components. 
We  should  note,  in  conclusion,  that  division  of  the  concentra- 
tion axis  according  to  atomic  per  cent  requires  an  additional 


TWO  COMPONENT  SYSTEMS.  107 

change.  We  are  aware  that  the  relative  quantity  of  eutectic, 
i.e.,  quantity  referred  to  a  unit  weight  total  substance,  is  a  linear 
function  of  the  concentration  expressed  in  weight  per  cent.  Obvi- 
ously this  relation  loses  its  validity  when  concentrations  are 
expressed  in  atomic  per  cent.  In  this  case,  the  quantity  by 
weight  of  eutectic  per  gram-atom  is  a  linear  function  of  the  con- 
centration. The  quantity  by  weight  of  eutectic  per  gram-atom 
may  be  experimentally  ascertained  by  noting  the  crystallization 
periods  at  the  eutectic  halting  points,  when  equal  numbers  of 
gram-atoms  are  taken  in  all  experiments.  If  the  relative  quan- 
tities of  eutectic  have  been  experimentally  ascertained  on  the 
basis  of  equal  quantities  of  material  by  weight  in  all  experiments, 
these  values  may  obviously  be  made  to  yield  the  quantities  of 
eutectic  on  the  basis  of  equal  numbers  of  gram-atoms,  by  recal- 
culation. This  was  done  in  constructing  the  fusion  diagram 
(Fig.  32)  from  Grube's  figures.  A  separate  recalculation  was  made 
for  each  horizontal. 

C.  Polymorphous  Transformations  do  not  Occur.  The  Components 
when  Fused  in  Conjunction  Unite  to  Form  a  Chemical  Com- 
pound which  does  not  Melt  Unchanged,  but  Decomposes  to  a 
Melt  and  a  Second  Crystalline  Variety  on  Heating  (Case  of  the 
Concealed  Maximum). 

Under  the  general  discussion  of  heterogeneous  equilibrium 
(from  p.  31),  we  encountered  an  example  of  a  compound  which 
failed  to  melt  unchanged,  and  we  learned  at  the  same  time  that 
such  a  process  must  occur  at  constant  temperature  (under  con- 
stant pressure). 

1.  FUSION  OF  GLAUBER'S  SALT,  Na2SO4  •  10  H2O.  — A  generally 
known  and  thoroughly  investigated  example  of  this  type  of 
fusion  is  offered  by  Glauber's  salt.  This  substance  melts  under 
atmospheric  pressure  at  32.4  degrees,  yielding,  instead  of  a  clear 
liquid,  a  pasty  mixture,  the  crystalline  constituent  of  which  is 
anhydrous  sodium  sulphate.  The  fused  portion  is  composed  of 
sodium  sulphate  and  water,  and  must  obviously  represent  a  satu- 
rated solution  of  Glauber's  salt  as  well  as  of  anhydrous  sodium 
sulphate.  For,  when  partial  fusion  is  effected,  and  the  system 
then  protected  from  loss  or  gain  of  heat,  both  crystalline  varieties 
are  capable  of  remaining  indefinitely  in  contact  with  the  melt 


108  THE  ELEMENTS  OF  METALLOGRAPHY. 

without  any  change  in  the  system  whatever.  The  system  is 
therefore  in  equilibrium;  a  condition  requiring  saturation  of  the 
solution  with  both  substances. 

We  describe  the  above  process  in  the  familiar  manner  by 
using  the  equation:  Na2SO4  '10H2O  <=^  Na2SO4  +  Saturated  Solu- 
tion (49.6  parts  water  per  100  parts  Na2S04),  in  which  the  arrows 
indicate  reversibility.  When  heat  is  added,  the  reaction  pro- 
ceeds from  left  to  right;  when  heat  is  abstracted,  it  proceeds  from 
right  to  left. 

We  have  here  a  condition  of  complete  heterogeneous  equilib- 
rium between  melt,  anhydrous  sodium  sulphate  and  Glauber's 
salt.  When  the  reaction  proceeds  from  left  to  right,  the  quantities 
of  anhydrous  sodium  sulphate  and  of  melt  increase,  the  compo- 
sition of  both  phases  remaining  unchanged.  We  are  already 
aware  that,  in  a  case  of  this  sort,  the  temperature  remains  constant 
during  addition  or  abstraction  of  heat  until  the  reaction  has  pro- 
ceeded to  completion.  The  temperature  32.4  degrees  therefore 
constitutes  a  limiting  temperature,  and  the  substance  under  con- 
sideration possesses  this  at  least  in  common  with  a  substance  which 
melts  without  decomposition,  viz.,  whose  melting  point  represents 
a  limiting  temperature  above  which  (under  atmospheric  pressure) 
the  liquid  state  alone  is  stable  and  below  which  the  crystalline 
state  alone  is  stable.  In  the  present  case,  Glauber's  salt  is  stable 
below  32.4  degrees,  while  a  mixture  of  anhydrous  sodium  sulphate 
and  its  saturated  solution  is  stable  above  this  limiting  tempera- 
ture. Both  crystalline  varieties  are  in  equilibrium  with  one 
another  and  with  a  solution  saturated  with  respect  to  both  at 
this  temperature  only. 

It  follows  from  the  above,  that  at  32.4  degrees,  Glauber's  salt 
and  sodium  sulphate  must  possess  the  same  solubility  in  water 
(figured  on  the  basis  of  the  common  constituent,  anhydrous 
sodium  sulphate).  For,  if  this  were  not  the  case, — if,  for 
example,  the  Glauber's  salt  possessed  a  greater  solubility  than  the 
anhydrous  sodium  sulphate  —  the  two  substances  could  not 
remain  in  equilibrium.  The  saturated  solution  of  Glauber's  salt 
would  then  be  supersaturated  with  respect  to  anhydrous  sodium 
sulphate,  and  would  of  necessity  proceed  to  deposit  the  latter 
until  this  condition  had  become  relieved.  At  this  point,  how- 
ever, the  solution  would  no  longer  be  saturated  with  Glauber's 


TWO  COMPONENT  SYSTEMS.  109 

salt  and  would,  in  consequence,  dissolve  the  salt  anew,  where- 
upon the  dissolved  material  would  again  separate  in  the  form  of 
anhydrous  sodium  sulphate,  etc.  This  process  would  continue 
until  all  of  the  Glauber's  salt  had  become  transformed  into  anhy- 
drous sodium  sulphate,  that  is  to  say,  under  these  conditions, 
Glauber's  salt  and  anhydrous  sodium  sulphate  would  not  be  in 
equilibrium;  on  the  contrary,  the  latter  alone  would  be  stable. 
Now,  this  is  actually  the  case  at  temperatures  above  32.4  degrees 
only,  and  we  conclude  that,  at  these  temperatures,  the  unstable 
Glauber's  salt  is  more  soluble  in  water  than  anhydrous  sodium 
sulphate.  Conversely,  at  temperatures  below  32.4  degrees,  the 
stable  Glauber's  salt  must  be  less  soluble  than  anhydrous  sodium 
sulphate.  In  other  words,  the  stable  crystalline  variety  invari- 
ably possesses  the  lesser  solubility.  The  two  varieties  possess  the 
same  solubility  at  the  equilibrium  temperature  alone  —  where 
both  are  stable.  At  this  temperature,  the  saturated  solution 
contains  49.6  parts  Na2SO4  and  100  parts  water.  These  figures 
are  from  LOWEL/  and  hold  equally  well  whether  water  is  satu- 
rated with  Glauber's  salt  or  with  anhydrous  sodium  sulphate. 
Lowel  was  also  able  to  prove  that  anhydrous  sodium  sulphate  is 
actually  much  more  soluble  than  Glauber's  salt  at  temperatures 
below  32.4  degrees.  A  saturated  Glauber's  salt  solution  pre- 
pared at  20  degrees  by  agitating  a  mixture  of  the  salt  and  water 
until  no  more  of  the  salt  dissolves,  or  by  allowing  a  solution 
which  has  previously  been  saturated  at  a  temperature  above 
20  degrees  to  remain  in  contact  with  Glauber's  salt  at  this  tem- 
perature until  the  salt  no  longer  separates  is  found  to  contain 
19.4  parts  anhydrous  sodium  sulphate  for  every  100  parts  water. 
But,  if  Glauber's  salt  is  fused  in  a  glass  vessel,  the  liquid  heated 
so  high  that  the  solution  above  the  separated  anhydrous  sodium 
sulphate  begins  to  boil,  the  vessel  then  closed  and  allowed  to  cool 
down  to  20  degrees,  this  solution  is  found  to  contain  52.76  parts 
anhydrous  sodium  sulphate  for  every  100  parts  water,  viz.,  nearly 
three  times  as  much  as  the  previous  solution  at  the  same  temper- 
ature. However,  the  crystalline  variety  in  contact  with  the 
liquid  in  the  latter  case  is  not  Glauber's  salt;  it  is  anhydrous 
sodium  sulphate,  which  has  separated  during  fusion  of  the  former. 
Hence,  the  figures  obtained  from  this  experiment  refer  to  the 
1  LOWEL,  Ann.  chim.  et  de  phys.  (3)  49,  50  (1857). 


110  THE  ELEMENTS  OF  METALLOGRAPHY. 

solubility  of  anhydrous  sodium  sulphate  in  water.  The  solution 
was  boiled  merely  to  dissolve  away  such  minute  crystals  of 
Glauber's  salt  as  may  have  adhered  to  the  cooler  walls  of  the  ves- 
sel. This  was  essential,  since  our  solution  was  supersaturated 
with  respect  to  Glauber's  salt,  and  merely  a  minute  crystal  of  the 
salt,  on  reaching  the  solution,  would  suffice  to  bring  about  imme- 
diate formation  (with  rise  in  temperature)  of  a  pasty  mixture  of 
Glauber's  salt  and  dilute  solution.  We  have  here  an  excellent 
example  of  the  saturation  of  a  solution  with  respect  to  one  crystal- 
line form,  and  its  supersaturation  with  respect  to  another  form. 
It  is  also  seen  at  once,  from  this  example,  that  the  form  which  is 
stable  under  certain  conditions  is  also  the  least  soluble  under 
these  very  conditions.  Above  32.4  degrees,  the  saturated 
Glauber's  salt  solution  would  obviously  be  supersaturated  with 
respect  to  anhydrous  sodium  sulphate.  Nevertheless,  it  is  ex- 
tremely difficult  to  prepare  such  a  solution.1 

It  is  clear  from  the  above  considerations  what  method  must  be 
adopted  in  practice  to  actually  realize  reversibility  of  the  reaction 
represented  by  the  equation: 

Na2SO4 .  10  H2O  <=>  Na2S04  +  Sat'd  Sol'n. 

The  reaction  proceeds  from  left  to  right,  in  measure  determined 
by  the  quantity  of  heat  added,  and  regardless  of  any  special  pre- 
cautionary measures.  If  it  be  required  that  the  reaction  proceed 
in  the  opposite  direction,  i.e.,  if  formation  of  Glauber's  salt  from 
anhydrous  sodium  sulphate  and  saturated  solution  be  prescribed, 
such  reaction  must  be  started  by  inoculation  of  the  solution  with 
a  crystal  of  Glauber's  salt. 

We  may  predict  the  following,  relative  to  cooling  processes 
which  will  take  place  in  mixtures  of  water  and  sodium  sulphate 
under  the  customary  assumption  that  equilibrium  invariably 
ensues  without  delay.  (This  signifies  a  resort  to  inoculation  in 
order  to  avoid  supersaturation.) 

(a)  If  the  mixture  corresponds  to  the  formula  Na2SO4 . 10  H2O, 

i.e.,  if  it  contains  78,9  parts  of  anhydrous  sodium  sulphate  for 

every  100  parts  water  (the  former,  partly  crystallized  and  partly 

dissolved),  then  the  total  quantity  of  anhydrous  sodium  sulphate 

1  TELDEN  and  SHENSTONE,  Phil.  Trans.,  175,  28  (1884). 


TWO  COMPONENT  SYSTEMS.  Ill 

will  react  with  the  solution  when  the  temperature  has  fallen  to 
32.4  degrees,  with  formation  of  Glauber's  salt.  The  temperature 
will  remain  constant  until  this  transformation  has  become  com- 
plete, when  all  the  material  will  have  crystallized.  Further  cool- 
ing is  unattended  by  heat  effect.  We  shall  have  a  single  halting 
point  upon  the  cooling  curve,  and  this  will  be  located  at  32.4 
degrees  (the  possible  appearance  of  breaks  is  neglected  in  this 
discussion). 

(6)  If  the  mixture  contains  more  than  78.9  parts  anhydrous 
sodium  sulphate  for  every  100  parts  water,  a  halting  point  will 
occur  at  32.4  degrees,  as  in  the  above  case.  However,  there  will 
not  be  sufficient  water  in  the  mixture  to  permit  transformation 
of  the  entire  quantity  of  anhydrous  sulphate  into  Glauber's  salt, 
and,  consequently,  when  the  reaction  has  proceeded  to  comple- 
tion, a  certain  quantity  of  the  former  will  still  remain.  But, 
withal,  after  the  equilibrium  temperature  32.4  degrees  has  been 
passed,  the  whole  material  will  have  become  crystalline,  so  that 
further  cooling  will  be  unattended  by  heat  effect.  As  in  the 
above  case,  we  shall  observe  a  single  halting  point  upon  the 
cooling  curve,  and  this  will  likewise  be  located  at  32.4  degrees. 

(c)  If,  on  the  other  hand,  the  mixture  contains  less  than 
78.9  parts  anhydrous  sodium  sulphate  (corresponding  to 
Na2SO4.  10  H2O),  but  more  than  49.6  parts  (corresponding  to 
the  saturated  solution  at  the  equilibrium  temperature,  32.4 
degrees),  then,  as  before,  anhydrous  sodium  sulphate  will  be 
present  with  saturated  solution  when  the  temperature  has  fallen 
to  32.4  degrees.  This  anhydrous  sodium  sulphate  must  then 
react  with  the  solution  to  form  Glauber's  salt.  We  shall,  there- 
fore, again  observe  a  period  of  constant  temperature  at  the  above 
point.  When  the  reaction  has  proceeded  to  completion,  however, 
not  all  of  the  material  will  have  crystallized.  That  is,  there  will 
be  more  water  in  the  mixture  than  corresponds  to  the  formula 
Na2SO4  .  10  H2O,  and,  consequently,  when  the  total  quantity  of 
anhydrous  sodium  sulphate  has  become  changed  to  Glauber's 
salt,  a  certain  quantity  of  saturated  solution  (at  32.4  degrees) 
must  remain.  On  further  cooling,  the  crystalline  variety  stable 
below  32.4  degrees  (Glauber's  salt)  will  separate  from  the  solution. 
This  process  is  accompanied  by  fall  in  temperature  and  will  con- 
tinue until  the  temperature  of  eutectic  crystallization  of  Glauber's 


112  THE  ELEMENTS  OF  METALLOGRAPHY. 

salt  and  water,  namely,  —  1.2  degrees,  has  been  attained.  The  solu- 
tion which  solidifies  without  change  in  composition  at  this  tem- 
perature to  a  mixture  of  Glauber's  salt  and  ice  crystals  contains 
four  parts  Na2SO4  for  every  100  parts  water. 

Cooling  curves  of  these  concentrations  will  thus  show  two  halt- 
ing points;  the  first,  at  32.4  degrees,  corresponds  to  transforma- 
tion of  anhydrous  sodium  sulphate  into  Glauber's  salt,  and  the 
second,  at  —1.2  degrees,  to  eutectic  crystallization  of  Glauber's 
salt-ice. 

(d)  If  the  mixture  contains  not  more  than  49.6  parts  sodium 
sulphate   (corresponding  to  saturation  at  the  equilibrium  tem- 
perature, 32.4  degrees),  and  not  less  than  four  parts  (correspond- 
ing to  the  composition  of  the  eutectic),  for  every  100  parts  water, 
then  no  anhydrous  sodium  sulphate  will  separate  at  32.4  degrees, 
since  the  solution  is,   at   most,   saturated   at  this  temperature. 
For  the  same  reason,  there  will  be  no  transformation  at  32.4 
degrees,  and  no  halting  point  upon  the  cooling  curve.     The  first 
separation  of  crystals  must  occur  below  32.4  degrees,  and  these 
will  be  crystals  of  Glauber's  salt,  the  variety  stable  below  this 
temperature,  and  therefore  the  less  soluble  variety.     The  tem- 
perature will  fall  continuously,  as  crystallization  of  Glauber's  salt 
proceeds,  until  the  eutectic  point   —1.2  degrees  is  reached.     At 
this  point,  the  remainder  of  the  solution  will  solidify  to  a  mix- 
ture of  Glauber's  salt  and  ice  crystals.     We  shall,  therefore,  ob- 
serve a  single  halting  point  upon  each  of  the  cooling  curves  of 
these  concentrations,  as  was  the  case  with  concentrations  a  and  6. 
But  the  halting  point  in  this  case  will  be  otherwise  located,  namely, 
at  —1.2  degrees,  the  temperature  of  eutectic  crystallization,  Glau- 
ber's salt-ice. 

(e)  Finally,  if  the  mixture  contains  less  than  four  parts  anhy- 
drous  sodium   sulphate    (corresponding   to    composition    of   the 
eutectic,   Glauber's  salt-ice)   for  every  100  parts  water,  ice  will 
separate  first,  as  we  have  learned  previously,  and  will  continue  to 
separate  until  the  solution  has  become  enriched  in  sodium  sul- 
phate up  to  the  eutectic  concentration.     Then  complete  crystalli- 
zation will  ensue,  as  above,  at  the  temperature    —1.2  degrees. 
The  cooling  curves  will  each  show  a  single  halting  point  at  —1.2 
degrees. 

We  have  seen  that  the  melting  point  of  Glauber's  salt  is  to  be 


TWO  COMPONENT  SYSTEMS.  113 

observed  in  all  sodium  sulphate-water  mixtures  containing  more 
than  49.6  parts  sodium  sulphate  for  every  100  parts  water.  Hence, 
this  temperature  is  admirably  adapted  to  use  as  a  thermometric 
fixed  point.  The  salt  is  easily  prepared  and  purified,  and  more- 
over, it  is  not  essential  in  this  connection  that  the  material  cor- 
respond very  closely  to  the  formula  Na2SO4 .  10  H20.  Glauber's 
salt  is  superior  for  this  purpose  to  any  salt  fusing  without  decom- 
position, since  the  melting  point  of  such  a  salt  must  represent  a 
maximum  upon  the  fusion  curve,  as  we  know,  and  will  be  lowered 
by  an  excess  of  either  component.  RICHARDS  and  WELLS1  have 
determined  this  point  with  great  accuracy.  The  value  which 
they  give  is  32.383  degrees.  Glauber's  salt  is  recommended  by 
them  as  a  most  simple  means  for  the  production  of  constant 
temperature.  In  this  connection,  it  is  obviously  superior  to  any 
thermostat.  Its  melting  point  is  less  dependent  upon  external 
pressure  than  the  melting  points  of  most  other  substances,  for 
reasons  which  we  shall  not  discuss  here. 

2.  GENERAL  CASE.  —  Let  the  components  of  the  system  — 
again  assumed  to  be  elements  —  and  their  melting  points  as  well 
be  denoted  by  A  and  B.  Let  AmBn  represent  the  formula  of  the 
compound,  and  t°  the  temperature  at  which  it  melts,  whereby  a 
liquid  and  a  second  crystalline  variety  are  produced.  If  we 
assume  on  account  of  simplicity  that  this  is  the  only  compound 
existing  between  the  two  elements,  then  the  crystalline  variety 
which  separates  during  fusion  must  be  either  pure  A  or  pure  B 
(pure,  in  accordance  with  our  leading  assumption  of  complete 
immiscibility  in  the  crystalline  state).  Suppose  that  it  be  the 
latter.  Then  the  equation  descriptive  of  this  reversible  process 
will  read: 

AmBn    <=»   aB  +  [mA+(n  -  a)  B]. 

crystals  crystals  melt 

Fusion,  i.e.,  progress  of  the  reaction  from  left  to  right,  is  effected 
by  heat  addition.  The  opposite  effect  is  secured  by  heat  abstraction. 
During  reaction,  the  quantities  of  the  several  phases  change,  but 
their  individual  composition  remains  constant:  throughout  the 
change  we  have  complete  equilibrium,  and  therefore  constant 

1  RICHARDS  and  WELLS,  Z.  phys.  Chem.,  43,  471  (1903). 


114  THE  ELEMENTS  OF  METALLOGRAPHY. 

temperature.  The  conditions  which  prevail  here  have  been  treated 
in  detail  in  the  preceding  discussion  (relative  to  Glauber's  salt). 
We  shall  now  proceed  to  apply  the  information  therein  presented 
to  the  general  case  in  terms  of  the  following  brief  outline : 

(1)  The  crystalline  variety  AmBn  is  stable  below  tf,  the  crystal- 
line variety  B  above  t°  and  both  crystalline  varieties  at  t°. 

(2)  Both  crystalline  varieties  B  and  AmBn  must  be  equally 
soluble  in  A  at  the  equilibrium  temperature  t°.     (Equal    solu- 
bility signifies  the  same  content  of  B,  the  common  constituent  of 
both  crystalline  varieties,  in  the  melt.)     For,  if  the  B-saturated 
A  solution  were  still  capable  of  dissolving  AmBn,  it  would  thereby 
become  supersaturated  with  respect  to  B,  and  continuous  solution 
of  AmBn,  attended  by  continuous  separation  of  corresponding 
amounts  of  B,  would,  of  necessity,  occur.     That  is  to  say,  there 
would   be   no   equilibrium.'    Under  these   conditions,    then,   the 
crystalline  variety  B  is  most  soluble  in  A  at  temperatures  above 
t°lt  where  it  is  the  stable  variety,  while  the  crystalline  variety 
AmBn  is  most  soluble  in  A  at  temperatures  below  tf,  where  it  is 
the  most  stable  variety  (we  obviously  imply  comparison  at  the 
same  temperature). 

(3)  Accordingly,  the  composition  of  the  melt  is  unequivocally 
defined  at  the  equilibrium  temperature.     This  melt  is  nothing 
other  than  a  saturated  solution  of  B  (and,  therefore,  of  AmBn)  in 
A  at  the  corresponding  temperature  ^. 

(4)  All     concentrations    which    are    B-richer    than    the    melt 
[mA  +  (n  —  a)  B],  saturated  at  tf,  must  show  halting  points 
upon  their  cooling  curves  at  the  temperature  tlt  since  all  of  them, 
with  exception  of  pure  B,  are  composed  of  crystalline  B  and  this 
melt  at  the  temperature  in  question,  and  become  either  com- 
pletely or  partially  transformed  into  AmBn,  according  to  the  pro- 
portion in  which  they  are  present. 

(5)  All  mixtures  which  are  A-richer  than  the  compound  AmBn 
must  show  halting  points  at  the  temperature  of  eutectic  crystal- 
lization of  AmBn  —  A.     We  shall  call  this  temperature  t2.     Con- 
centrations which  are  richer  in  B  than  AmBn  fail  to  show  this 
halting  point.     It  is  clear  that  those  concentrations  which  are 
intermediate   between   AmBn   and   the   saturated   melt   [mA  + 
(n  —  a)  B]  will  show  halting  points  at  t°,  as  well  as  at  t2°. 

The  diagram  shown  in  Fig.  33  represents  such  mutual  relations 


TWO  COMPONENT  SYSTEMS. 


115 


between  two  substances  as  we  have  just  discussed:  its  essential 
properties  are  ordered  according  to  the  above  stipulations.  It  is 
apparent  at  the  start  that  no  maximum  can  appear  upon  the 
fusion  curve  at  the  concentration  which  corresponds  to  the  com- 


10      20     30      40      50 
Weight  per  cent  B 


60      70      80      90     100 
AniBn 


FIG.  33. 


position  of  the  compound,  since  such  a  maximum  melting  point 
is  the  especial  characteristic  of  a  compound  which  fuses  without 
decomposition.  But,  instead,  a  horizontal  DC  must  meet  the 
fusion  curve  at  the  concentration  D,  corresponding  to  the  com- 
position of  the  melt  [mA  +  (n  —  a)  B].  This  horizontal  extends 
to  pure  J9,  according  to  (4)  above,  and  corresponds  to  the  halting 
points  at  t°  upon  the  cooling  curves. 


116  THE   ELEMENTS   OF   METALLOGRAPHY. 

Upon  adding  a  certain  quantity  of  A  to  molten  B,  the  melting 
point  of  the  latter  is  lowered.  This  is  indicated  by  the  branch  BD. 
The  crystalline  variety  B  crystallizes  first  upon  cooling  melts 
which  are  intermediate  in  concentration  between  B  and  D.  Crys- 
tallization begins  at  that  point  upon  the  curve  branch  BD  which 
corresponds  to  the  concentration  of  the  melt.  Incomplete  equi- 
librium obtains  along  BD]  as  pure  B  separates,  the  tempera- 
ture sinks  along  BD,  corresponding  to  the  continually  increa- 
sing A-content  of  the  melt,  until,  at  length,  the  temperature 
ti  is  reached  (at  concentration  D).  Upon  further  heat  ab- 
straction, B  crystals  and  melt  react  with  formation  of  the  com- 
pound AmBn. 

The  process  described  by  the  reaction  given  on  p.  114  therefore 
proceeds  from  right  to  left.  We  will  now  assume  that  this  reac- 
tion proceeds  to  completion.  (The  earlier  considerations,  relative 
to  Glauber's  salt,  were  also  based  upon  this  assumption.)  Then 
the  reaction,  and  consequently  the  period  of  constant  tempera- 
ture determined  by  it,  will  continue  until  either  crystalline  B  or 
melt  —  according  to  whether  the  former  or  the  latter  is  present 
in  excess  —  shall  have  become  exhausted.  Not  until  the  con- 
centration corresponds  exactly  to  the  composition  of  the  com- 
pound AmBn  (=  h),  will  melt  and  crystalline  B  be  present  in 
such  quantities  that  both  will  have  become  exhausted  after  com- 
pletion of  the  reaction,  and  the  melt  have  solidified  as  a  whole 
to  AmBn.  Concentrations  located  between  100  (=  pure  B)  and 
h  (=  AmBn)  will  still  contain  an  excess  of  crystalline  B  after 
transformation  has  ceased,  and  will  therefore  be  wholly  crystal- 
lized at  this  point.  On  the  other  hand,  concentrations  located 
between  D  and  h  must,  after  complete  exhaustion  of  the  B  crys- 
tals, still  contain  an  excess  of  melt,  which  will  continue  to  crys- 
tallize along  the  curve  branch  DC.  It  is  the  compound  AmBn, 
however,  which  separates  primarily  along  this  branch,  since  we 
are  now  within  its  temperature  range  of  stability,  namely,  below 
t°.  The  end  point  C  of  the  branch  DC  is  determined  by  intersection 
of  this  branch  with  the  branch  AC.  We  reflect  here  that  the 
melting  point  of  A  is  lowered  by  addition  of  B  (or,  what  amounts 
to  the  same  thing,  of  AmBn).  This  lowering  is  shown  by  the 
branch  AC,  representing  primary  separation  of  A  and  enrich- 
ment of  the  melt  in  AmBn.  Thus,  the  point  of  intersection  C  of 


TWO  COMPONENT  SYSTEMS.  117 

AC  and  DC  corresponds  to  the  eutectic  point  —  where  the  melt 
is  saturated  with  both  crystalline  varieties.  Accordingly,  these 
two  varieties  separate  simultaneously  at  the  temperature  of  C, 
in  the  proportions  indicated  by  its  concentration.  Eutectic  crys- 
tallization at  the  point  C  (temperature  t2)  will  obviously  occur 
in  all  concentrations  containing  a  lesser  quantity  of  B  than 
corresponds  to  AmBn.  Consequently,  the  eutectic  horizontal 
aCb  extends  from  concentration  0  (  =  pure  A)  to  concentration 
h  (=  AmBn). 

According  to  the  above,  the  following  cooling  curves  correspond 
to  the  various  concentrations  of  our  diagram: 

(1)  A  melt  of  concentration  0,  corresponding  to  pure  A,  crys- 
tallizes as  a  whole  at  the  constant  temperature  A.     Its  cooling 
curve  accordingly  shows  a  single  halting  point,  located  at  A. 

(2)  Melts  which  are   intermediate  in  concentration    between 
0   and   C   separate    A    primarily.      Crystallization   follows   the 
branch  AC,  having  begun  at  that  point  upon  this  branch  which 
corresponds  to  the  concentration  in  question.     When  the  melt 
has  become  enriched  in  AmBn  up  to  the  concentration  of  the 
eutectic  C,  its  temperature  will  have  fallen  to  t2°,  and  eutectic 
crystallization,   characterized  by  simultaneous  separation  of  A 
and  AmBn  crystals  at  constant  temperature,  thereupon  ensues. 
A  break,  as  well  as  a  halting  point,  the  latter  at  t2°,  will  be  found 
upon  these  cooling  curves. 

(3)  Melts  which   are   intermediate   in   concentration   between 
C  and   D  separate   AmBn   primarily.     Crystallization  of  AmBn 
follows  the  branch  DC.     When  the  melt  has  become  enriched  in 
A  up  to  concentration  C,  eutectic  crystallization  ensues  at  t2°,  as 
in  the  previous  case.     We  shall  again  have  a  break  and  a  halting 
point  upon  each  cooling  curve,  the  latter  at  t2°. 

(4)  Melts  which  are  intermediate  in  concentration  between  D 
and  h  (  =  AmBn)   separate  B  primarily.     Crystallization  follows 
the  branch  BD.     The  melt  becomes  continually  A-richer  and  its 
temperature  constantly  falls,  as  B  separates.     When  the  concen- 
tration D  has  been  attained,  the  temperature  will  have  fallen  to 
if,  and  the  melt  will  have  become  saturated  with  both  B  and 
AmBn.     At  this  point  transformation  of  B  +  melt  into  the  new 
crystalline  variety  occurs.     The  temperature  remains  constant 
at  tj°  until  the  end  of  transformation.     A  certain  quantity  of 


118  THE  ELEMENTS   OF  METALLOGRAPHY. 

melt  will  then  remain,  as  we  have  seen  above.  This  will  separate 
AmBn  crystals  along  the  branch  DC  with  continuous  fall  in 
temperature,  until  it  has  become  enriched  in  A  up  to  the  eutectic 
concentration  C.  By  this  time,  the  temperature  will  have  fallen 
to  t2°,  and  a  second  period  of  constant  temperature  will  now  be 
observed,  namely,  that  corresponding  to  eutectic  crystallization 
at  C.  At  its  conclusion,  the  whole  alloy  will  be  crystallized. 
According  to  the  above,  cooling  curves  of  these  concentrations 
will  be  characterized  by  a  break  and  two  halting  points,  the  latter 
located  at  t°  and  t2°  respectively. 

(5)  A  melt  of  concentration  h,  corresponding  to  the  pure  com- 
pound AmBn,  also  separates  B  primarily  along  the  branch  ED. 
The  initial  temperature  of  crystallization  is  given  by  the  inter- 
section of  the  (projected)  dotted  line  hi  with  DB.     When  the 
melt   has   reached   the   concentration   and   temperature   of   the 
point  Z),  owing  to  continuous  separation  of  B,  transformation  of 
B  +  melt  into  the  crystalline  variety  AmBn  takes  place.     At  the 
conclusion   of   this   transformation,   the   whole   alloy   will   have 
become  crystalline,  and  AmBn  will  alone  be  present.     The  cool- 
ing   curve   of   this    concentration,    which    represents    the    pure 
compound  AmBn,  will,  therefore,  show  a  break,   and  a  halting 
point  at  t°.     Such  a  break,  situated   above  the  halting  point, 
serves  to  differentiate  the  cooling  curve  of  a  compound  which 
melts  under  decomposition  from  that  of  a  compound  which  melts 
unchanged. 

(6)  Melts   which   are   intermediate   in   concentration   between 
h  (=  AmBn)  and  100  (=  B)  also  separate  B  at  the  start.     When 
the  concentration  and  temperature  of  such  a  melt  have  fallen  to 
the  values  defined  by  the  point  D,  transformation  of  B  +  melt 
into  AmBn  takes  place.     In  this  case,  however,  more  B  is  now 
present  than  can  react  with  the  melt,  whence,  B  crystals  are  found 
with  AmBn  crystals  in  the  solid  alloy  after  transformation.     At 
all  events,  the  cooling  curves  which  correspond  to  these  concen- 
trations  also   show  breaks,  and   halting   points   at   t°n  and  are 
obviously  comparable  to  the  cooling  curve  of  the  pure  compound 
in  this  respect. 

(7)  A  melt  of  concentration   100   (corresponding  to  pure  B) 
solidifies  completely  at  the  constant  temperature  B.     A  single 
halting  point,  at  B,  is  found  upon  its  cooling  curve. 


TWO  COMPONENT  SYSTEMS.  119 

The  diagram  is  characterized  first  of  all  by  the  three  branches 
which  compose  the  fusion  curve,  namely,  AC,  CD  and  DB;  none  of 
them  possessing  a  maximum.  Each  branch  corresponds  to  pri- 
mary separation  of  an  individual  crystalline  variety.  Here,  the 
three  varieties  are  A,  AmBn  and  B. 

As  a  second  characteristic,  we  have  the  appearance  of  two 
horizontals  (of  constant  temperature)  both  of  which  cover  the 
same  concentration  range  for  a  certain  distance.  The  horizontal 
aCb  passes  through  the  eutectic  point  C,  and  is,  therefore  an 
eutectic  horizontal.  It  extends  from  concentration  0  (corre- 
sponding to  pure  A)  to  the  concentration  of  the  compound  AmBn. 
The  relative  quantity  of  eutectic  has  a  maximum  value  1  at  the 
point  C,  and  decreases  lineally  toward  the  zero  value  of  both 
end  points.  Upon  erecting  verticals  above  the  eutectic  horizontal 
as  base  line,  at  lengths  which  are  proportional  to  the  relative 
quantities  of  eutectic  throughout  the  different  concentrations 
(and  to  the  eutectic  periods  of  constant  temperature),  and  joining 
their  end  points,  two  straight  lines  da  and  db  are  obtained.  The 
first  of  these  intersects  the  horizontal  at  the  point  a,  corresponding 
to  pure  A,  and  the  second,  at  the  point  6,  corresponding  to  the 
compound  AmBn. 

The  second  horizontal  extends  from  the  break  D  upon  the 
fusion  curve  to  concentration  100  (corresponding  to  pure  B). 
This  is  also  commonly  called  an  eutectic  horizontal.  In  com- 
mon with  the  actual  eutectic  horizontal,  this  horizontal  of  con- 
stant temperature  represents  equilibrium  between  two  crystalline 
varieties  and  melt.  But,  along  the  actual  eutectic  horizontal,  we 
have  the  concentration  of  melt  situated  between  the  concentra- 
tions of  the  two  crystalline  varieties  with  which  it  is  in  equilib- 
rium; on  this  account,  the  melt  is  invariably  exhausted  when 
crystallization  is  brought  about  by  abstraction  of  heat.  In  the 
other  case,  the  melt  is  richer  in  one  constituent  (A,  in  the  present 
instance)  than  the  two  crystalline  varieties  with  which  it  is  in 
•equilibrium,  and,  when  crystallization  of  the  melt  is  effected  by 
heat  abstraction,  the  crystalline  variety  which  differs  most  in 
composition  from  this  melt  (here  B)  is  utilized,  as  we  have  seen, 
in  forming  the  crystalline  variety  of  intermediate  composition 
(here  AmBn).  Thus,  when  a  melt  solidifies  eutectically,  two 
crystalline  varieties  are  formed,  but  in  a  case  of  this  sort  a  new 


120  THE  ELEMENTS   OF   METALLOGRAPHY. 

crystalline  variety  is  formed  from  melt  and  a  variety  already 
present,  and  it  must  depend  upon  the  quantitative  relations 
between  melt  and  the  crystalline  variety  first  separated,  whether 
or  not  a  balance  of  melt  will  remain  after  completion  of  the 
reaction. 

Now,  the  relative  quantity  of  the  variety  AmBn,  formed  by 
reaction  between  B  and  melt,  is  obviously  at  its  maximum  1  in 
the  concentration  which  corresponds  exactly  to  the  formula 
AmBn.  In  all  other  concentrations,  an  excess  of  either  A  or  B 
will  be  present  after  reaction.  If  B  is  present  after  reaction,  i.e., 
if  the  concentration  of  the  original  alloy  is  situated  between 
h  (  =  AmBn)  and  100  (  =  #),  then  the  relative  quantity  of  AmBn 
which  can  be  formed  will  be  directly  proportional  to  the  per- 
centage content  of  A  in  the  alloy.  Consequently,  this  quantity 
decreases  lineally  between  concentrations  h  and  100  from  a  maxi- 
mum 1  to  0.  If,  on  the  other  hand,  the  total  quantity  of  crystal- 
line B  is  exhausted  during  reaction,  and  an  excess  of  liquid 
remains,  i.e.,  if  the  concentration  of  the  original  alloy  is  situated 
between  h  (  =  AmBn)  and  D  (concentration  of  the  break),  then 
the  relative  quantity  of  AmBn  produced  will  be  proportional  to 
the  relative  quantity  of  B  which  has  separated  primarily  by  the 
time  the  temperature  has  fallen  to  t°  and  the  composition  of  the 
residual  melt  has  been  brought  to  concentration  D.  But  this 
latter  quantity  is  proportional  to  the  difference  in  5-content 
between  the  alloy  under  consideration  and  melt  of  composition  D. 
Therefore,  the  relative  quantity  of  AmBn  produced  will  decrease 
lineally  between  concentration  AmBn  and  D  from  a  maximum  1  to 
0.  If  the  concentration  of  the  original  alloy  is  equal  to,  or 
A-richer  than,  D,  it  is  clear,  as  a  matter  of  course,  that  no  AmBn 
will  be  formed  by  reaction  between  B  and  melt,  since  no  B  can  have 
separated.  Separation  of  AmBn  from  such  melts  occurs  directly. 
The  relative  quantity  of  AmBn  produced  by  reaction  between 
crystalline  B  and  melt  in  the  different  concentrations  is  shown 
in  the  usual  manner  along  the  horizontal  DC.  The  periods  of 
constant  temperature  at  tf  upon  the  cooling  curves  are  (under 
the  customary  assumptions)  proportional  to  these  relative  quan- 
tities. 

The  entire  concentration-temperature  diagram  is  divided  into 
seven  fields  of  condition  by  the  curves  and  straight  lines.  Of 


TWO  COMPONENT  SYSTEMS.  121 

these  fields,  one  represents  melt,  a  second,  third  and  fourth  are 
fields  with  one  crystalline  variety,  and  a  fifth,  sixth  and  seventh, 
fields  with  two  crystalline  varieties. 

The  fields  of  condition  are  characterized  by  the  following  prop- 
erties: 

(1)  Above  the  fusion  curve  ACDB  all  is  liquid. 

(2)  In   the   triangle   ACa,  the   crystalline   variety  A,   having 
separated  primarily  along  the  curve  branch  AC,  is  in  equilibrium 
with  melt. 

(3)  In  the  field  DCbi,  the  crystalline  variety  AmBn  is  in  equilib- 
rium with  melt.     Separation  of  AmBn  from  concentrations  which 
are  A-richer  than  D  takes  place  exclusively  along    DC,   viz., 
directly.     Separation  of  AmBn  from   concentrations  which   are 
5-richer  than  D  occurs  as  a  result  of  reaction  between  primarily 
separated  B  and  melt. 

(4)  In  the  triangle  BDc,  the  crystalline  variety  B,  having  sepa- 
rated primarily  along  BD,  is  in  equilibrium  with  melt. 

(5)  The  rectangle  aCkf  is  the  field  of  primarily  separated  A  and 
eutectic  C  —  composed  of  A  and  AmBn. 

(6)  The  rectangle  Cbhk  is  the  field  of  AmBn  crystals,  either 
separated  directly  or  produced  as  a  result  of  reaction  between  B 
and  melt,  and  eutectic  C. 

(7)  The  rectangle  cihg  is  the  field  of  primarily  separated  B 
crystals  and  AmBn  crystals  —  separated  directly  or  produced  as 
a  result  of  reaction  between  B  and  melt. 

The  structure  of  sections  from  the  reguli  must  of  course  cor- 
respond with  the  thermal  results.  Accordingly,  in  concentrations 
located  between  0  (=  pure  A)  and  k  (=  C),  we  shall  observe 
primarily  separated  A,  surrounded  by  eutectic  C.  The  quantity 
of  eutectic  increases  with  the  B-content.  Solidified  alloys  of  con- 
centration k  consist  entirely  of  eutectic  C.  In  concentrations 
located  between  k  (=  C)  and  h  (=  AmBn),  the  same  eutectic 
must  occur  as  in  preceding  concentrations.  It  decreases  in  quan- 
tity with  increasing  5-content.  We  have  here  a  different  crystal- 
line variety  imbedded  in  the  eutectic,  namely,  AmBn.  A  section 
of  composition  h,  corresponding  to  the  pure  compound  AmBn, 
must  be  entirely  composed  of  the  crystalline  variety  AmBn.  In 


122  THE  ELEMENTS   OF   METALLOGRAPHY. 

sections  which  contain  more  B  than  corresponds  to  the  compound 
AmBn,  i.e.,  which  are  intermediate  in  composition  between  h 
and  100,  the  primarily  separated  B  will  have  been  incompletely 
transformed  into  AmBn,  and,  consequently,  this  unaltered  B 
material  is  surrounded  by  the  more  recently  formed  compound 
AmBn.  The  structure  of  these  sections  differs  from  that  of  the 
preceding  ones  in  that  the  primarily  separated  crystalline  variety 
B  is  not  imbedded  in  an  eutectic,  but,  rather,  in  a  structure 
element,  which,  even  under  the  highest  powers,  proves  to  be  homo- 
geneous —  cannot  be  resolved  into  two  constituents.  Concentra- 
tions 0  (pure  A)  and  100  (pure  B)  must  obviously  present  the 
homogeneous  appearance  of  a  pure  substance. 

The  following  may  be  said  relative  to  the  geometrical  form  of 
the  fusion  curve: 

It  follows  from  the  stability  relations  (see  p.  114)  that,  at  tem- 
peratures above  t°,  the  crystalline  variety  B,  and,  at  tempera- 
tures below  tj0,  the  crystalline  variety  AmBn,  must  possess  the 
lesser  solubility  in  A,  or,  what  amounts  to  the  same  thing,  that 
above  t°,  a  melt  in  equilibrium  with  5,  and  below  tf,  a  melt  in 
equilibrium  with  AmBn,  must  show  the  lesser  5-content. 

Thus,  when  we  prolong  the  curve  branches  BD  and  CD  beyond 
D,  as  is  done  in  Fig.  33,  both  prolongations  must  correspond  to 
B-richer  concentrations  than  does  the  (full)  curve  branch  of 
stable  equilibrium,  which  relation  is  plainly  shown  in  the  figure. 
That  is  to  say,  prolongation  of  a  curve  branch  beyond  its  end 
point  signifies  continuation  of  the  equilibrium  between  the  crys- 
talline variety  separating  along  the  respective  curve  and  melt  into 
a  field  where  this  crystalline  variety  is  no  longer  stable.  We 
have  seen  in  the  Glauber's  salt  example  that  unstable  condi- 
tions of  this  sort  may  actually  be  realized.  Hence,  the  above 
construction  is  justified  by  experimental  results.  It  follows, 
however,  from  the  fact  that  these  dotted  prolongations  corre- 
spond to  unstable  conditions,  that  the  points  of  these  dotted 
lines  must  lie  at  higher  B  concentrations  than  the  points  of  the 
(full)  curve  branches  of  stable  equilibrium  for  corresponding  tem- 
peratures—  for  the  very  reason  that,  on  theoretical  grounds, 
the  greater  solubility  must  be  conceded  to  the  unstable  crys- 
talline variety  A.  Similarly,  the  unstable  character  of  the  dotted 
curve  branches  is  evidenced  by  the  fact  that  the  points  of  these 


TWO  COMPONENT  SYSTEMS. 


123 


curves  lie  at  lower  temperatures  than  the  points  of  the  full 
branches  for  corresponding  concentrations  (corresponding  to 
supercooled  conditions). 

Thus  we  see  that  BD  and  CD  cannot  pass  continuously  into 
one  another,  but  must  intersect  at  D.  Moreover,  an  apex  directed 
toward  the  solid  field  must  occur  at  this  point,  i.e.,  DB  must  run 
steeper  than  CD  at  D.  Culmination  of  these  branches  (CD  and 
DB)  in  an  apex  directed  toward  the  liquid  field,  as  shown  in 
Fig.  34  at  D,  is  impossible  from  the  present  considerations,  for 
we  perceive  at  once  that,  in  such  case,  the  dotted  prolongations 
of  the  two  curve  branches  would  necessarily  represent  stable  con- 
ditions of  equilibrium.  If  the  experimental  investigation  points 
to  such  disposition  of  the  curve  branches,  the  reason  must  be 
sought  in  inaccurate  measurements.  At  length,  the  difference  in 
solubility  between  the  two  crystalline  varieties  may  be  very  incon- 
siderable. In  such  event,  the  branches  CD  and  BD  will  obviously 


FIG.  34. 


FIG.  35. 


differ  so  slightly  in  direction  that  the  angular  intersection  at  D, 
required  by  theory,  will  fail  to  show  on  the  experimentally  deter- 
mined fusion  curve  (Fig.  35).  Incidence  of  the  horizontal  DC  at 


124  THE  ELEMENTS  OF  METALLOGRAPHY. 

D  will  then  constitute  the  only  indication  of  a  break  at  this 
point. 

In  Fig.  33,  the  curve  branch  CD  is  continued  beyond  D,  accord- 
ing to  the  relations  which  would  obtain  if  the  compound  were 
fusible  without  decomposition.  We  are  aware  that  a  maximum 
would  be  expected  at  the  concentration  of  the  compound  AmBn 
in  such  case.  This  maximum  fails  of  appearance,  since  it  is 
covered,  or  concealed,  by  the  curve  branch  BD,  corresponding 
to  the  crystalline  variety  B  which  is  stable  within  this  tempera- 
ture interval.  For  this  reason,  the  present  case,  representing 
fusion  of  a  compound  with  separation  of  a  new  crystalline  variety, 
is  also  called  the  case  of  the  "  concealed  maximum." 

Our  fusion  diagram  is  characterized,  on  the  one  hand,  by  a 
fusion  curve  consisting  of  three  branches  without  maximum,  and, 
on  the  other  hand,  by  two  constant  temperature  horizontals  par- 
tially covering  one  another.  Conversely,  if  on  constructing  the 
fusion  diagram  of  a  two  component  system  from  experimental 
data,  we  meet  these  characteristic  properties,  it  is  permissible 
to  conclude  that  the  two  substances  are  completely  miscible 
in  the  liquid  state  and  completely  immiscible  in  the  crystalline 
state;  that  they  sustain  no  polymorphous  transformation  which  is 
accompanied  by  appreciable  heat  effect;  and  that,  under  the  cus- 
tomary limitations,  they  unite  to  form  a  single  chemical  compound, 
which  does  not  melt  unchanged,  but  decomposes  at  a  definite 
temperature  into  melt  and  another  crystalline  variety  —  in  this 
case,  one  of  the  two  pure  components  of  the  system.  According  to 
TAMMANN/  two  expedients,  both  of  them  resting  upon  determi- 
nation of  the  periods  of  the  halting  points  upon  the  cooling  curves 
are  available  in  fixing  the  composition  of  the  compound: 

(1)  The  quantities  of  eutectic  C  along  the  eutectic  horizontal 
aCb,  and,  consequently,  the  duration  of  the  eutectic  periods  of 
constant  temperature,  reach  the  zero  value  at  the  point  6,  repre- 
senting the  concentration  of  the  pure  compound  AmBn. 

(2)  The  maximum  of  the  periods  of  constant  temperature  along 
the  horizontal  DC  occurs  at  the  point  i,  representing  the  concen- 
tration of  the  compound  AmBn,  since,  at  this  point,  the  whole 
alloy  solidifies  uniformly  to  AmBn. 

1  TAMMANN,  Z.  anorg.  Chem.,  37,  303  (1903). 


TWO  COMPONENT  SYSTEMS.  125 

The  fusion  curve  can  play  no  part  in  the  determination  of  the 
composition  of  the  compound,  as  it  possesses  no  maximum.  It 
should  be  particularly  noted  that,  in  general,  the  break  D  upon 
the  fusion  curve  does  not  correspond  to  the  composition  of  the 
compound. 

The  first  check  upon  the  composition  of  the  compound,  as 
ascertained  by  use  of  these  two  criteria,  consists  in  obtaining 
satisfactory  agreement  between  the  results.  Then  again,  micro- 
scopic investigation  of  a  section  corresponding  in  composition  to 
the  pure  compound  should  reveal  the  presence  of  a  single  struc- 
ture element.  Conformity  of  the  composition  of  the  compound 
to  the  law  of  multiple  proportions,  i.e.,  its  representation  by  a 
comparatively  simple  formula,  is  not  of  especial  significance  as  a 
check  upon  the  results,  as  was  shown  on  p.  87,  but  may  serve  in 
certain  cases  by  way  of  lending  additional  support  to  the  mature 
conclusions. 

The  rule  given  on  p.  88,  namely,  that  the  number  of  com- 
pounds is  equal  to  the  number  of  branches  of  the  fusion  curve 
diminished  by  two,  is  also  valid  here,  but  is  of  no  practical  service 
when  the  break  D  upon  the  fusion  curve  is  not  well  marked,  and 
may  therefore  escape  observation,  as  is  frequently  the  case. 
The  other  rule  introduced  at  the  same  time,  namely,  that  the 
number  of  compounds  is  equal  to  the  number  of  eutectic  hori- 
zontals diminished  by  one,  is  valid  only  when  we  regard  DC  as  an 
eutectic  horizontal,  and  extend  our  conception  of  the  term  eutec- 
tic horizontal  to  cover  any  horizontal  along  which  two  crystalline 
varieties  are  in  equilibrium  with  melt. 

3.  SODIUM-BISMUTH  ALLOYS.  —  The  Sodium-Bismuth  System, 
studied  by  MA-THEWSON,*  may  serve  as  an  example  of  the  general 
case  developed  in  the  preceding  section.  It  is  true  that  sodium  and 
bismuth  form  a  compound  which  melts  unchanged,  in  addition  to 
the  one  which  melts  under  decomposition.  This  is  seen  at  once 
in  the  diagram  (Fig.  36).  However,  complete  analogy  to  the 
above  conditions  is  found  in  that  part  of  the  diagram  which  lies 
to  the  right  of  the  dotted  vertical  Bax. 

Concentrations  are  expressed  in  atomic  per  cent.  Small 
crosses  are  used  in  entering  observed  temperatures. 

1  MATHEWSON,  Z.  anorg.  Chem.,  50,  187  (1906). 


126  THE  ELEMENTS   OF  METALLOGRAPHY. 

Certain  details  may  be  noted  as  follows:  The  fusion  curve  is 
composed  of  three  branches,  namely,  ABC,  CD  and  DE.  The 
first  branch  possesses  a  maximum  at  B.  Since  two  compounds, 
and  therefore  four  different  crystalline  varieties,  including  pure 
sodium  and  pure  bismuth,  appear  in  this  system,  a  fusion  curve 
of  four  branches  is  to  be  expected.  Here  again,  one  branch  of 
the  fusion  curve  is  dwarfed  into  insignificance  (see  pp.  72  and  89). 
In  the  present  instance,  this  is  the  branch  corresponding  to  pri- 
mary separation  of  sodium.  The  melting  point  of  sodium,  which 
was  found  to  be  97.5  degrees  according  to  the  table  given  by 
Mathewson  (I.  c.),  is  raised  by  the  first  appreciable  additions  of 
bismuth.  The  temperature  of  eutectic  crystallization  along  the 
horizontal  Aa  is  practically  identical  with  the  melting  point  of  pure 
sodium,  whence,  the  eutectic  consists  of  practically  pure  sodium. 

The  formula  Na3Bi  of  the  compound  which  melts  unchanged  at 
775  degrees  is  deduced  as  follows:  At  the  concentration  25 
atomic  per  cent  Bi  are  located: 

(1)  the  maximum  B  of  the  curve  branch  ABC, 

(2)  the  end  point  a  of  the  eutectic  horizontal  Aa,  and 

(3)  the  end  point  c'  of  the  horizontal  Ccc'  (445  degrees).     (The 
lengths  of  the  halting  point  periods  are  shown  in  the  customary 
manner   by   construction   of   verticals   upon   the    corresponding 
horizontal.) 

The  formula  of  the  compound  which  melts  under  decompo- 
sition at  445  degrees  is  determined  from  the  following  data: 

(1)  The  maximum  of   the   periods  along  the   horizontal  Ccc' 
(445  degrees)  is  located  at  the  concentration  c  =  49.7  atomic  per 
cent  sodium. 

(2)  The   end   point   D   of   the   eutectic   horizontal   dDd'  (218 
degrees)  is  located  at  50.6  atomic  per  cent  sodium. 

The  mean  of  these  determinations  is  50.15  atomic  per  cent 
sodium,  a  value  which  corresponds,  within  a  rational  error 
limit,  to  the  formula  NaBi. 

According  to  the  diagrammatic  evidence,  this  compound  melts 
at  the  temperature  of  the  horizontal  Ccc'  =  445  degrees  to  a  liquid 
of  concentration  C,  with  separation  of  the  crystalline  variety 
Na3Bi.  This  process  is  described  quantitatively  by  the  equation: 
1  NaBi  «=*  0.06  Na3Bi+Melt  (0.82  Na+0.94  Bi  =  53  at.  per  cent  Bi). 


TWO  COMPONENT  SYSTEMS. 


127 


Atomic  per  cent  Bismuth 


NaBi 


0  10  20  30  40  50 


Weight  per  cent  Sodium 


FIG.  36.     Fusion  Diagram  of  Sodium-Bismuth  Alloys  according  to 
Mathewson. 


128  THE  ELEMENTS   OF  METALLOGRAPHY. 

As  is  apparent  from  this  equation,  the  quantity  of  compound 
Na3Bi  which  appears  as  residue  after  fusion  is  very  small.  Thus, 
the  composition  of  the  melt  differs  very  little,  in  this  case,  from 
that  of  the  pure  compound:  the  melt  is  merely  some  3  per  cent 
Bi-richer  than  the  compound,  as  shown  by  the  diagram.  This 
condition  is  responsible  for  a  phenomenon  which  may,  under  cer- 
tain circumstances,  prove  troublesome  in  practice.  We  observe 
that  the  periods  along  the  horizontal  Ccc'  (Fig.  36)  have  not 
reached  the  zero  value  at  the  point  C,  as  is  the  case  with  the 
periods  along  the  horizontal  DC  at  the  corresponding  point  D  in 
the  ideal  diagram  (Fig.  33).  As  a  matter  of  fact,  the  latter  con- 
dition must  always  obtain,  since  an  alloy  of  the  composition 
represented  by  the  point  of  change  in  direction  of  the  fusion  curve 
melts  to  an  homogeneous  liquid  (no  second  crystalline  phase 
appears).  But  when,  as  in  the  present  case,  the  composition  of 
the  melt  C  differs  only  slightly  from  that  of  the  pure  compound, 
its  cooling  curve  will  also  appear  closely  similar  to  that  of  a  pure 
substance,  i.e.,  it  will  run  approximately  horizontal  for  a  time 
during  solidification.  (C/.  the  curve  for  2J  per  cent  NaCl  in 
Fig.  9a.)  For  this  reason,  it  is  not  possible  in  the  present  case  to 
distinguish  between  the  heat  effect  which  corresponds  to  forma- 
tion of  the  compound  NaBi  from  the  previously  separated  crys- 
talline variety  Na3Bi  and  melt,  and  that  which  is  due  to  direct 
separation  of  the  compound  NaBi  from  melt  of  concentration  C, 
as  long  as  such  separation  occurs  at  practically  the  same  temper- 
ature. It  may  happen,  particularly  when  the  curve  branch  CD 
runs  almost  horizontally  into  C,  that  no  decrease  in  the  halting 
periods  is  evident  just  after  their  maximum  value  has  been  attained. 
Obviously,  determination  of  the  composition  of  the  compound 
by  locating  the  maximum  of  the  halting  periods  along  the  respec- 
tive horizontal  is  unusually  difficult  in  such  cases. 

The  melting  point  of  bismuth  E  (273  degrees)  is  lowered  along 
ED  by  addition  of  sodium  as  far  as  the  eutectic  point  D  (218 
degrees). 

Since  these  alloys  are  extremely  unstable  in  the  air,  sections 
could  not  be  prepared  in  the  usual  manner,  and  it  was  necessary 
to  use  freshly  prepared  cleavage  surfaces  for  the  direct  examina- 
tion. The  appearance  of  these  samples  substantiated  the  results 
of  thermal  analysis. 


TWO  COMPONENT  SYSTEMS.  129 

4.  GOLD-ANTIMONY  ALLOYS.  —  The  fusion  diagram  of  the  Gold- 
Antimony  System,  as  contributed  by  VOGEL/  is  given  in  Fig.  37. 

Concentrations  are  expressed  in  weight  per  cent. 

The  fusion  curve  is  composed  of  the  three  branches  AB,  BC 
and  CD,  which  correspond  to  primary  separation  of  the  three 
respective  crystalline  varieties,  pure  gold,  pure  compound  and 
pure  antimony.  Since  no  maximum  is  to  be  observed  upon  any 
one  of  the  three  branches,  we  are  forced  to  conclude,  according  to 
previous  considerations,  that  the  compound  does  not  fuse  un- 
changed, but  decomposes  into  melt  and  another  crystalline 
variety  —  in  this  case,  antimony  —  at  the  temperature  of  the 
horizontal  Cd.  This  fails,  however,  to  represent  the  actual  con- 
ditions, as  is  seen  on  considering  the  halting  periods  along  the 
two  horizontals.  We  have  here  the  remarkable  case  in  which 
the  composition  of  the  compound  practically  corresponds  with  the 
concentration  of  the  break  C  upon  the  fusion  curve.  This  case 
may  be  regarded  as  a  limiting  case  of  either  of  the  two  pre- 
viously considered  general  cases.  Thus,  reasoning  from  the 
case  of  the  concealed  maximum  (Fig.  33,  p.  115),  we  assume 
that  the  point  i,  corresponding  to  the  concentration  of  the 
pure  compound  AmBn,  advances  along  the  horizontal  DC  up  to 
a  position  of  coincidence  with  D.  Reasoning  from  the  case  of 
the  open  maximum  (Fig.  16c,  p.  78),  we  assume  that  one  arm 
CE  of  the  curve  branch  DCE  becomes  continually  smaller  and 
finally  disappears  when  the  maximum  C  and  the  eutectic  point  E 
coincide. 

The  formula  of  the  compound  AuSb2  (54.93  per  cent  Sb)  is 
fixed  as  follows: 

(1)  The  periods  of  crystallization  at  the  temperature  of  the 
horizontal  Cd  (460  degrees)  increase  as  gold  is  added  to  antimony, 
reaching  a  maximum  at  55  per  cent  Sb. 

(2)  The    halting   periods    along   the   eutectic    horizontal    aDc 
(360  degrees)  decrease  from  B  toward  c,  reaching  the  zero  value 
at  55  per  cent  Sb. 

(3)  The  cooling  curve  of  an  alloy  containing  55  per  cent  Sb 
possesses  one  halting  point  only  —  located  at  460  degrees.     Such 
an  alloy  crystallizes  after  the  manner  of  a  pure  substance. 

1  VOGEL,  Z.  anorg.  Chem.,  50,  151  (1906). 


130  THE  ELEMENTS   OF  METALLOGRAPHY. 

Au 


1100 


1000' 


900' 


800° 


Sb 


Liquid  Field 


600C 


500C 


400C 


300C 


200C 


100* 


AuSb 


\ 


Melt 


Melt 


+Mclt 


\ 


Au 


Sb+A 


uSb, 


E\ 


tectic 


0         10         20         30          40         50         60         70          80         90       100 

Weight  per  cent 

0     10      20      30        40        50          60  70  80  90  100 

Atomic  per  cent 

FIG.  37.     Fusion  Diagram  of  Gold-Antimony  Alloys  according  to  Vogel. 


TWO  COMPONENT  SYSTEMS.  131 

(4)  A  section  containing  55  per  cent  Sb  presents  a  completely 
homogeneous  appearance. 

We  note  here  that  the  curve  branch  BC  enters  at  C  horizontally. 
Although,  strictly  considered,  the  horizontal  Cd  ends  at  C  (see 
p.  128),  its  horizontal  course  in  this  vicinity  leads  to  the  ob- 
servation of  halting  points  upon  the  cooling  curves  of  alloys 
containing  less  antimony  than  corresponds  to  the  point  C  (one 
containing  50  per  cent  Sb,  for  example)  at  temperatures  which  are 
practically  identical  with  that  of  the  horizontal  Cd  (460  degrees). 
This  is  shown  in  the  diagram  by  a  dotted  line  beginning  at  i,  con- 
centration C,  and  falling  away  toward  the  left. 

A  description  of  the  crystallization  processes  which  occur  upon 
cooling  the  melts  of  various  concentrations  follows: 

(1)  A   melt   of   concentration    (0  =  pure   gold)    solidifies    uni- 
formly at  the  point  A  (=  1064  degrees). 

(2)  Pure  gold  separates  primarily  along  the  curve  branch  AB, 
from  concentrations  which  are  located  between  0  and  /  (=  B}. 
This  separation  commences  at  that  point  of  the  branch  which  cor- 
responds  to   the   respective    concentration.     The    melt   becomes 
enriched  in  antimony,  as  the  temperature  of  solidification  con- 
tinues to  fall,  until  the  concentration  B  is  reached.     Then  the 
temperature  will  have  fallen  to  360  degrees,  and  eutectic  crystal- 
lization will  ensue.     The  eutectic  consists  of  pure  gold  and  the 
compound  AuSb2. 

(3)  A   melt   of   concentration  /=  B   solidifies   eutectically    at 
360  degrees. 

(4)  The  compound  AuSb2  separates  primarily  along  the  curve 
branch    CB,    from    concentrations    which    are    located    between 
/(=  B)  and  g  (=  C).     During  this  process,  the  gold  content  of 
the   melt   increases,   and   the   temperature   of  solidification   falls 
until  the  point  B  is  reached.     Here,  the  remainder  of  the  melt 
crystallizes  eutectically. 

(5)  A  melt  of  concentration  g,  corresponding  to  the  pure  com- 
pound AuSb2,  solidifies  uniformly  at  the  temperature  C  =  460 
degrees. 

(6)  Concentrations  which  are  intermediate  between  g   (=  C) 
and    100  separate   pure  antimony   along  the  curve  branch  DC. 
The  gold-content  increases  as  the  temperature  of   solidification 
falls,   until  the  point  C,   corresponding  to  the  pure  compound 


132 


THE  ELEMENTS   OF   METALLOGRAPHY. 


AuSb2,  is  reached.  The  remainder  of  the  melt  then  solidifies 
uniformly  at  constant  temperature  (460  degrees)  to  crystals  of 
the  pure  compound  AuSb2.  Thus,  we  have  a  single  crystalline 
variety  instead  of  eutectic  —  a  practically  pure  substance  at  any 
rate — as  secondary  element  throughout  this  concentration  interval. 
(7)  A  melt  of  concentration  100  (=  pure  Sb)  solidifies  uniformly 
at  the  temperature  D  (=  631  degrees). 


FIG.  38.     80%  Au  +  20%  Sb,  etched  with  NaOH.     Magnified  27  times. 

The  concentration-temperature  plane  embraces  seven  fields  of 
condition,  which  are  summarized  in  Table  5. 

TABLE  5. 
Fields  of  Condition. 

I.   Liquid  Field:  bounded  below  by  the  Fusion  Curve  ABCD 
II.   Fields  with  one  crystalline  variety  +  melt: 


ABa 
BCc 
CDd 

III.   Fields  with  1 
aBfe 

Au 
AuSb2 
Sb 

,wo  crystalline  varieties: 
Au  +  Eutectic  (Au  +  AuSb2) 
AuSb2  +  Eutectic  (Au  +  AuSb2) 
Sb  +  AuSb2 

The  thermal  evidence  is  generally  substantiated  by  the  struc- 
ture of  the  sections.     Fig.  38  represents  a  section  containing  20 


TWO  COMPONENT  SYSTEMS.  133 

per  cent  Sb,  magnified  27  times.  This  section  was  etched  by  long- 
continued  action  of  caustic  soda.  The  primarily  separated  gold 
crystals  have  remained  bright  during  etching:  they  are  situated 
side  by  side  in  rectilinear  chains  which  form  crosses  with  one 
another.  Light  gold  particles,  and  dark  etched  particles  per- 
taining to  the  compound  AuSb2  —  in  reality  colored  red  —  are 
to  be  plainly  seen  in  the  eutectic  which  surrounds  the  primary 
gold  crystals.  The  structure  of  the  eutectic  appears  to  much 


FIG.  39.     75%  Au  +  25%  Sb,  etched  with  NaOH.     Magnified  70  times. 

better  advantage  in  Fig.  39,  which  represents  a  section  contain- 
ing 25  per  cent  Sb,  i.e.,  very  close  to  the  eutectic  concentration 
(24  per  cent  Sb).  This  section  is  magnified  70  times.  Caustic 
soda  was  also  used  in  this  case.  The  lamellar  structure  of  the 
eutectic  is  apparent,  particularly  in  the  right-hand  portion  of 
the  figure. 

Fig.  40  shows  another  section,  also  etched  with  caustic  soda. 
This  contains  40  per  cent  Sb  and  is  magnified  70  times. 
According  to  the  evidence  of  the  diagram,  primarily  separated 
crystals  of  the  compound  AuSb2  must  show  in  this  picture.  These 
appear  as  reddish  (black  in  the  photograph)  crystalline  polygons, 
quadratic  in  shape,  and  show  enclosures  of  eutectic  in  many 
instances.  The  secondary  structure  element  must  be  the  same 


134  THE   ELEMENTS   OF   METALLOGRAPHY. 

eutectic  B  here,  as  in  the  previous  sections.  This,  however,  can- 
not be  decided  from  the  figure.  It  appears  equally  bright  all  over 
the  surface,  and  gives  no  evidence  of  dual  composition.  The 
etching  may  have  been  less  energetic  in  this  case  than  before, 
resulting  in  little  or  no  action  upon  the  compound  AuSb2  con- 
tained in  the  eutectic.  We  may,  of  course,  assume  that  the  com- 
pound which  is  associated  with  gold  eutectically  is  protected 


FIG.  40.     60%  Au +40%  Sb,  etched  with  NaOH.     Magnified  70  times. 

from  the  action  of  the  etching  agent  by  the  surrounding  gold, 
and  is  therefore  less  attacked  than  the  primarily  separated  crys- 
tals of  the  same  composition. 

Fig.  41  represents  a  section  containing  60  per  cent  Sb,  magni- 
fied 22  times.  According  to  the  diagrammatic  evidence,  a  small 
quantity  of  antimony  must  have  separated  primarily  in  this 
concentration.  Accordingly,  we  note  dark-colored  antimony 
crystals  of  dendritic  form  with  rounded  edges,  imbedded  in  a 
homogeneous  mass  of  bright  compound.  Aqua  regia  was  used 
in  etching.  This  reagent  fails  to  attack  the  compound,  when 
used  with  care. 

5.  INCOMPLETE  PROGRESS  OF  THE  DECOMPOSITION.  —  Thus 
far,  we  have  dealt  exclusively  with  reactions  which  proceed  to 
completion,  i.e.,  we  have  considered  that  equilibrium  between 
the  'separate  phases  in  all  parts  of  the  system  can  be  consum- 
mated with  all  necessary  rapidity.  This  requirement  will,  from 


TWO  COMPONENT  SYSTEMS.  135 

the  very  nature  of  things,  be  realized  during  decomposition  of 
the  compound  on  heating.  Here,  the  progress  of  the  reaction  is 
such  that  the  compound  decomposes  into  melt  and  a  new  crystal- 
line variety.  Quite  different  are  the  relations  when  the  compound 
is  formed.  In  this  case,  the  crystalline  variety  stable  at  the 
higher  temperature  reacts  with  melt,  on  cooling,  to  produce  the 
compound  in  question,  and,  where  the  reaction  must  proceed 


^ 


FIG.  41.     40%  Au  +  60%  Sb,  etched  with  aqua  regia.     Magnified  22  times. 

completely  within  a  short  period  of  time,  it  is  obviously  necessary 
that  the  first  crystalline  variety  come  in  contact  with  the  melt. 
Such  contact  may  be  hindered  in  various  ways. 

We  may  imagine,  for  example,  that  the  resulting  compound  be 
deposited  as  a  layer  upon  the  surface  of  the  first  crystalline 
variety,  and  in  this  manner  practically  prevent  the  melt  from 
coming  in  contact  with  the  latter  and  reacting  completely  with 
it.  A  very  slight  quantity  of  compound  —  practically  negligible 
—  might  possibly  suffice  to  produce  this  effect.  Since,  however, 
such  " total  envelopment"  has  not  as  yet  been  observed,  we  need 
not  attempt  to  discuss  it. 

On  the  other  hand,  envelopment  may  be  incomplete.  Sub- 
joining our  reasoning  to  the  general  case  presented  on  p.  113, 
suppose  we  assume  that  the  protection  afforded  the  primarily 
separated  B  crystals  by  envelopment  with  the  compound  A  Bn, 
is  so  effective  that,  with  sufficient  quantities  of  melt,  in  maximo, 


136  THE  ELEMENTS   OF  METALLOGRAPHY. 

only  half  of  the  B  crystals  can  sustain  transformation  into  AmBn 
crystals.  Then  the  equation, 

aB  +  [mA  +  (n  -  a)  B]  =  AmBn 

melt  D 

(see  p.  113),  does  not  correctly  describe  the  reaction  between 
B  and  melt.  In  reality,  according  to  our  assumption  that  only 
half  of  B  can  become  transformed,  the  process  conforms  to  the 
equation, 

2  aB  +  [mA  +  (n  —  a)  B]  =  AmBn  +  aB. 

melt  D 

Thus  it  follows  that  thermal  investigation  cannot  lead  to  the 
correct  formula  of  the  compound,  AmBn,  but  yields,  rather,  the 
formula  AmBn+a:  for  the  maximum  quantity  of  compound  is 
formed  when  the  concentration  corresponds  to  the  stochiometri- 
cal  relations  given  by  our  equation.  Change  in  quantity  of 
either  B  or  melt  effects  decrease  of  AmBn.  We  shall,  therefore, 
find  the  maximum  of  crystallization  periods  along  the  horizontal 
DC  (Fig.  33)  displaced  from  its  normal  position  at  the  concentra- 
tion AmBn,  to  the  concentration  AmBn  +  aB,  which  equals 
AmBn+a.  The  eutectic  horizontal  aCb  also  ends  at  this  concen- 
tration, since,  at  this  point,  as  well  as  in  all  J5-richer  concentra- 
tions, complete  exhaustion  of  melt  occurs. 

These  considerations  appear  to  show  that,  in  case  of  a  concealed 
maximum,  deduction  of  the  same  formula  for  the  compound 
by  ascertaining  the  maximum  of  crystallization  periods  along 
the  horizontal  DC  as  by  ascertaining  the  end  point  6  of  the 
eutectic  horizontal  aCb  in  itself  fails  to  guarantee  that  this 
formula  will  actually  correspond  to  the  composition  of  the  com- 
pound. We  can  merely  affirm,  on  the  basis  of  the  experimental 
results,  that  the  composition  of  the  compound  lies  between  D  and 
the  maximum  of  halting  periods  along  DC. 

At  this  point,  however,  microscopical  investigation  is  of  assist- 
ance. Thus,  if  the  reaction  has  proceeded  to  completion,  an 
alloy  of  concentration  i,  the  location  of  the  maximum  of  halting 
periods  along  DC  (Fig.  33),  must  appear  completely  homogene- 
ous, as  we  have  seen  (since  it  is  composed  exclusively  of  pure 
compound  AmBn).  Alloys  of  all  concentrations  between  i  and  D 
may  contain  two,  and  only  two,  structure  elements,  namely,  the 
compound  AmBn  and  the  eutectic  C.  If,  on  the  other  hand, 


TWO  COMPONENT  SYSTEMS.  137 

envelopment  has  occurred,  the  maximum  i  of  crystallization 
periods  along  DC  does  not  coincide  with  the  composition  of  the 
compound  AmBn,  but  lies  further  toward  the  B  side,  and,  con- 
sequently, an  alloy  of  the  composition  of  this  maximum  cannot  be 
homogeneous;  it  must  contain  two  structure  elements,  primarily 
separated  B  crystals  as  nucleii,  surrounded  by  AmBn  crystals. 
Alloys  of  concentrations  between  i  and  D  must  show  three  struc- 
ture elements,  —  embracing  eutectic  C,  in  addition  to  the  two 
previously  enumerated. 

The  presence  of  three  structure  elements  in  one  section  has 
not  been  encountered  up  to  the  present.  We  have  become 
familiar  with  those  cases  alone  in  which  the  solidified  alloy  shows 
two  structure  elements.  The  contingency  that  three  structure 
elements  appear  in  one  section  depends  upon  a  more  or  less  con- 


FIG.  42.     42%  Pd  +  58%Pb,  etched  with  dilute  nitric 
acid.     Magnified  70  times. 

strained  protection  of  one  structure  element  from  contact  with 
the  melt.  Normally,  viz.,  when  equilibrium  has  become  perfectly 
established,  not  more  than  two  structure  elements  appear  in  any 
section  of  an  alloy  composed  of  two  metals.  We  therefore  charac- 
terize a  structure  corresponding  to  the  above  as  abnormal.  The 
upper  portion  of  Fig.  42,  which  shows  a  section  composed  of 
42  per  cent  palladium  and  58  per  cent  lead,  etched  with  dilute 
hydrochloric  acid,  reveals  abnormal  structure  of  this  sort.  A 


138  THE  ELEMENTS   OF   METALLOGRAPHY. 

dark  nucleus  of  the  primarily  separated  crystalline  variety  (cor- 
responding to  B)  is  to  be  seen  l  surrounded  by  a  zone  of  the  new 
crystalline  variety  (corresponding  to  AmBn),  itself,  in  turn,  sur- 
rounded by  eutectic  of  coarsely  granular  structure. 

According  to  the  above,  the  formula  of  a  compound  melting 
under  decomposition,  as  determined  thermally,  can  be  regarded 
as  conclusive  only  when  microscopical  investigation  supplies  proof 
of  normal  structure.  Now,  all  systems  thus  far  investigated  in 
which  a  concealed  maximum  occurs  and  the  maximum  i  of  crys- 
tallization periods  along  the  horizontal  DC  (Fig.  33)  corresponds 
in  concentration  with  the  end  point  b  of  the  eutectic  horizontal 
aCb  reveal  perfectly  normal  structure  under  the  microscope, 
whence  it  is  clear  that  reaction  has  been  complete.  Where  reac- 
tion has  been  incomplete,  however,  the  eutectic  horizontal  aCb 
invariably  fails  to  end  at  the  concentration  of  the  maximum  i  of 
crystallization  periods  along  DC,  but  extends  beyond  this  point. 
Hence,  we  conclude  that  incompleteness  of  reaction  is  not  due 
exclusively  to  envelopment. 

A  further  cause  of  incomplete  reaction  may  consist  in  unequal 
distribution  of  the  primarily  separated  crystalline  variety  in  the 
melt,  just  at  the  point  of  reaction.  The  crystals  may  have  settled 
more  or  less  to  the  bottom  of  the  reaction  vessel  (segregation). 
In  such  event,  reaction  will  be  incomplete  in  certain  portions  of 
the  mixture  —  above,  in  the  present  case  —  owing  to  early  ex- 
haustion by  the  melt  of  the  inadequate  quantity  of  B  crystals 
which  are  available.  Other  portions  of  the  mixture  —  below,  in 
this  particular  instance  —  react  incompletely,  on  account  of 
insufficient  melt  and  excess  of  B  crystals.  Thus,  the  conse- 
quence of  such  derangement  is  incomplete  exhaustion  of  B  crys- 
tals, as  well  as  of  melt,  within  certain  intervals  of  concentration. 
Considering,  first  of  all,  the  rather  simple  case  wherein  the  same 
proportion — one-half — of  the  theoretically  possible  quantity  of 
crystals  and  melt  is  transformed  in  all  concentrations  (between 
D  and  c),  we  must  alter  the  equation, 

aB  +  [mA  +  (n  -  a)  B]  =  AmBn, 

melt  D 

to, 

aB  +  [mA  +  (n  -  a)  B]  =  J  AmBn  +  J  aB  +  J  [mA  +  (n  -  a)  B]. 

melt  D  melt  D 

1  RUER,  Z.  anorg.  Chem.,  52,  345  (1907). 


TWO  COMPONENT  SYSTEMS.  139 

Since  the  proportion  by  weight  between  B  and  melt  remains 
the  same  in  the  latter  equation,  no  displacement  of  the  maximum 
of  crystallization  periods  along  DC  follows.  The  verticals  in 
Fig.  33,  which  are  proportional  to  these  crystallization  periods, 
must,  however,  be  shortened  one-half,  corresponding  to  forma- 
tion of  only  half  of  the  theoretical  quantity  of  compound  in  all 
cases.  Thus,  the  increase  in  period  of  crystallization  along  DC 
from  D  to  i,  and  from  c  to  i,  remains  linear,  and  we  shall  accord- 
ingly expect  a  sharp  maximum  at  concentration  i,  corresponding 
to  composition  of  the  compound  AmBn.  On  the  other  hand, 
according  to  our  assumption,  half  of  the  melt  remains  unex- 
hausted in  all  concentrations,  and,  therefore,  gives  rise  to  eutectic 
crystallization  at  C.  Hence,  the  eutectic  horizontal  aCb  must 
extend  throughout  the  whole  diagram  —  up  to  100  per  cent  B. 
It  thus  appears  that,  of  the  two  criteria  used  for  determination  of 
the  composition  of  a  compound  AmBn,  the  first,  which  consists 
in  location  of  the  maximum  along  DC,  retains  its  application  under 
the  present  conditions,  while  the  second,  which  consists  in  loca- 
tion of  the  end  point  d  of  the  eutectic  horizontal  aCb,  fails. 

Relative  to  an  extension  of  these  results  to  actual  conditions,  it 
is  at  once  clear  that  the  irregularities  caused  by  uneven  distribu- 
tion of  B  in  the  melt  will  be  confined  to  the  central  portion  of 
the  horizontal  DC.  As  long  as  melt  is  present  to  considerable 
excess,  namely,  in  concentrations  from  D  to  i  (Fig.  43),  segregation 
of  B  crystals  in  the  lower  portion  of  the  containing  vessel  will  not 
prevent  their  complete  exhaustion  by  the  melt.  On  account  of 
the  excess  quantity  of  melt,  each  B  crystal  will,  even  under  these 
conditions,  articulate  with  enough  melt  to  effect  its  normal  trans- 
formation. The  point  /  approaches  closer  to  D,  in  proportion  as 
the  irregular  distribution  of  B  crystals  in  the  melt  becomes  em- 
phasized. On  the  other  side  of  i,  the  point  m  represents  the 
limit  of  abnormality.  In  all  concentrations  located  between  c 
and  m,  the  separated  crystalline  variety  B  is  present  in  such 
excess  that  the  melt  is  invariably  exhausted,  notwithstanding 
uneven  distribution.  Thus,  the  diagram  suffers  no  alteration 
between  D  and  I  on  the  one  hand,  and  between  m  and  c  on  the 
other  hand. 

Formation  of  AmBn  falls  somewhat  below  the  theoretical  amount 
between  I  and  m.  The  influence  of  irregular  distribution  of 


140 


THE  ELEMENTS   OF   METALLOGRAPHY. 


B  crystals  in  melt  must  become  more  noticeable  in  proportion 
as  the  excess  of  the  predominating  component  diminishes;  that 
is  to  say,  in  proportion  as  we  approach  the  concentration  of  pure 
AmBn  from  either  side.  Consequently,  a  more  and  more  gradual 
increase  in  the  period  of  crystallization  along  DC  will  result  as  we 
pass  from  I  to  the  maximum  i,  as  well  as  from  m  to  i.  On  this 
account,  the  curve  Dec,  joining  the  corresponding  verticals,  will 


90      100 


Weight  per  cent  B 

FIG.  43. 


AinBn 


fail  to  show  a  sharp  point,  as  in  Fig.  33,  but  will  culminate  in  a 
flat  summit,  as  represented  in  Fig.  43.  The  position  of  this  maxi- 
mum must,  however,  remain  unaltered.  It  coincides  with  the 
concentration  of  the  pure  compound  AmBn.  The  eutectic  hori- 
zontal aCb  (Fig.  43)  reaches  on  beyond  the  maximum  as  far  as 
that  concentration  in  which  the  first  trace  of  melt  fails  to  react 


TWO  COMPONENT   SYSTEMS.  141 

with  the  B  crystals:  as  far  as  concentration  m,  in  terms  of  our 
special  assumption. 

These  deductions  are  in  complete  harmony  with  the  experi- 
mental facts.  Incomplete  progress  of  the  transformation,  for  the 
most  part,  effects  no  alteration  in  the  position  of  the  maximum  of 
crystallization  periods  along  DC.  Such  position  agrees  with  the 
concentration  of  the  compound  AmBn.  However,  on  account  of 
the  imperfectly  marked  character  of  the  maximum,  its  position  is, 
in  general,  difficult  of  determination.  There  are  cases  in  which 
the  periods  along  DC  between  I  and  m  remain  equal  within  the 
experimental  error  limit.  In  certain  cases,  the  maximum  may 
still  be  determined  with  a  tolerable  degree  of  accuracy.  Such 
determination  then  constitutes  a  valuable  indication  of  the  com- 
position of  the  compound.  On  the  other  hand,  the  eutectic 
horizontal  in  these  cases  invariably  reaches  beyond  the  concentra- 
tion of  the  compound,  whereby  this  means  of  check  upon  the  com- 
position of  the  compound  is  lost.  The  structure  of  the  sections 
will  be  abnormal,  in  the  sense  that,  in  certain  portions,  we  shall 
observe  primarily  separated  B  crystals,  surrounded  by  crystals  of 
the  compound  AmBn,  while,  in  other  portions,  we  shall  see  crys- 
tals of  the  compound,  surrounded  by  eutectic. 

Obviously,  it  is  also  possible  for  segregation  and  envelopment 
to  appear  in  close  association.  The  resulting  complications  may 
be  appreciated  from  the  above  without  difficulty. 

We  take  note  here  of  the  obvious  fact  that  a  fusion  diagram 
corresponding  to  incomplete  reaction,  as  above,  is  in  complete 
agreement  with  Fig.  33  from  concentration  0  (=  pure  A)  as  far 
as  concentration  D,  since  the  abnormalties  due  to  envelopment, 
segregation,  etc.,  can  only  appear  between  D  and  100  per  cent  B. 
This  is  made  evident  by  the  relative  quantities  of  eutectic  shown 
along  the  horizontal  aCb  (Fig.  43).  These  quantities  decrease 
lineally  toward  AmBn  from  concentration  C  to  concentration  D 
(or  to  the  respective  concentration  at  which  abnormality  begins), 
and,  in  principle  at  least,  the  dotted  prolongation  from  dn  to  the 
point  of  intersection  o  with  the  eutectic  horizontal  aCb  always 
serves  for  determination  of  the  composition  of  the  compound 
AmBn.  We  have  seen,  however,  in  earlier  examples  that  the 
eutectic  halting  periods  are  not  invariably  proportional  to  the 
eutectic  quantities  from  an  experimental  standpoint,  whence  it 


142  THE  ELEMENTS   OF  METALLOGRAPHY. 

appears  that  too  much  reliance  should  not  be  placed  upon  such 
determination,  unless  verified  by  independent  means. 

We  see  from  the  above  that  incomplete  progress  of  reaction, 
whatever  its  cause,  operates  effectively  against  accurate  determi- 
nation of  the  composition  of  a  compound.  The  maximum  of 
crystallization  periods  is  often  imperfectly  developed,  and  there- 
fore difficult  to  determine.  Again,  we  have  no  guarantee  that  its 
concentration  coincides  with  the  composition  of  the  compound, 
as  in  normal  cases,  where  homogeneous  structure  of  the  alloy  in 
question  testifies  to  this  effect.  Verification  of  the  result  on  the 
basis  of  the  second  criterion,  which  calls  for  location  of  the  eutec- 
tic  end  point  b  (horizontal  aCb)  at  the  concentration  of  the  com- 
pound, is  also  excluded,  for,  as  we  have  seen,  the  eutectic  line 
extends  beyond  this  concentration.  It  is,  therefore,  particularly 
fortunate  that  complete  progress  of  the  reaction  may  be  super- 
induced in  certain  cases,  as  pointed  out  by  TAMMANN.*  To  this 
effect,  the  cooled  alloy  is  first  pulverized,  whereby  it  is  brought 
into  a  state  of  comparative  uniformity,  previously  enclosed 
crystals  being  opened  up.  This  material  is  thereupon  heated 
almost  to  the  transformation  temperature,  and  maintained  there 
for  some  time.  In  this  way,  B  crystals  and  melt  are  frequently 
led  to  react  further,  with  formation  of  AmBn.  If  this  process  is 
effectual,  the  mixture  on  cooling  will  no  longer  show  eutectic 
crystallization,  except  in  such  concentrations  as  are  ^4-richer  than 
AmBn,  i.e.,  in  those  concentrations  which  must  still  contain  melt 
after  complete  disappearance  of  B.  Thus,  the  eutectic  horizontal 
aCb  now  ends  at  the  concentration  of  the  compound,  and  may 
serve  in  the  determination  of  its  composition.  The  structure  of 
the  section  must  be  normal,  and  a  section  of  the  concentration  of 
the  compound  AmBn  must  appear  homogeneous  under  the  micro- 
scope. Finally,  the  maximum  of  halting  periods  along  DC  may 
also  be  accurately  ascertained  by  taking  heating  curves.  All 
criteria  and  checking  methods  pertaining  to  the  normal  case  are 
thus  available.  When  the  above-mentioned  expedient  fails  of 
results,  the  problem  of  accurately  fixing  the  composition  of  the 
compound  must  be  left  unsolved,  as  far  as  our  present  methods 
are  concerned.  (Compare,  for  example,  R.  Sahmen,  Kupfer- 
Kadmiumlegierungen,  Z.  anorg.  Chem.,  49,  301  (1906).) 

1  TAMMANN,  Z.  anorg.  Chem.,  47,  296  (1905). 


TWO  COMPONENT  SYSTEMS.  143 

D.  Changes  in  the  Crystalline  State. 

Up  to  the  present,  our  attention  has  been  confined  to  such 
two  component  systems  as  sustain  no  further  change  after  solidifi- 
cation. That  alloys  may  undergo  change  after  solidification  has 
occurred  is,  however,  clearly  proven  by  thermal  investigation. 
This  condition  is  by  no  means  infrequent,  and  such  changes  are 
often  accompanied  by  very  considerable  heat  effects.  Two  rea- 
sons may  be  given  for  these  changes.  In  the  first  place,  a  single 
crystalline  variety  may  become  transformed  into  another  variety 
which  is  stable  at  some  lower  temperature.  We  are  already 
familiar  with  a  process  of  this  sort  under  the  title  polymorphous 
transformation.  On  the  other  hand,  cases  are  known  wherein 
two  crystalline  varieties  react  upon  each  other  with  formation 
of  a  third  variety:  a  chemical  compound.  This  phenomenon 
is  at  variance  with  common  experience,  as  well  as  with  the  old 
rule:  ''Corpora  non  agunt  nisi  fluida."  The  rate  at  which  a 
substance  diffuses  when  dissolved  in  a  solid  body  is  in  general 
so  slow  that,  even  though  the  possibility  of  reaction  between 
two  crystalline  substances  be  directly  conceded,  such  reaction 
can  hardly  be  expected  to  make  much  progress  in  a  short  time. 
The  sum  total  of  our  experience  in  these  matters  leads  to  the 
belief  that  an  extremely  intimate  contact,  or  molecular  inter- 
penetration,  of  the  substances  in  question  is  pre-essential  to 
chemical  reaction,  and  such  a  condition  can  be  realized  in  the 
case  of  solid  bodies  only  as  a  result  of  reciprocal  diffusion.  As 
a  matter  of  fact,  certain  examples  may  be  adduced  to  show  that 
the  capability  of  solid  bodies  to  diffuse  may  be  rather  con- 
siderable at  high  temperatures.  In  general,  reactions  in  the  solid 
state  appear  to  become  possible  only  when  the  reacting  sub- 
stances are  noticeably  soluble  in  one  another.  We  shall,  how- 
ever, refrain  from  all  critical  discussion  of  these  phenomena, 
the  mechanism  of  which  have  not  as  yet  been  adequately 
investigated,  be  content  to  consider  the  possibility  of  reaction 
between  two  crystalline  varieties  with  formation  of  a  third  as 
settled,  even  though  it  constitute  an  unexpected  experimental 
development. 

Now,  it  is  easily  possible,  as  TAMMANN  has  pointed  out,1  to 
1  TAMMANN,  Z.  anorg.  Chem.,  47,  296  (1905). 


144 


THE   ELEMENTS   OF  METALLOGRAPHY. 


distinguish  between  polymorphous  transformation  and  chemical 
reaction  whereby  two  crystalline  varieties  combine  to  form  a 
third  on  cooling. 

Polymorphous  transformation  is  characterized  by  the  altera- 
tion of  a  given  crystalline  variety  in  such  manner  that  another 
variety  is  formed  without  change  in  composition.  Transforma- 
tion of  this  sort  occurs  at  constant  temperature  in  the  case  of  a 
pure  substance,  as  explained  on  p.  11,  and  as  follows  at  once  from 
the  text  on  p.  32.  Since  we  have  excluded  solubility  in  the  crystal- 
line state  from  present  considerations,  the  crystalline  variety  sus- 
taining polymorphous  transformation  is  to  be  regarded  as  pure. 
Its  transformation  will,  therefore,  invariably  occur  at  the  same 
temperature,  and  in  all  concentrations  where  it  is  present,  whether 
as  primary  structure  element,  or  as  constituent  of  an  eutectic. 
The  heat  effect  is  of  course  proportional  to  the  quantity  of  mate- 
rial which  undergoes  transformation.  Thus,  cooling  curves  made 

under  the  usual  conditions  will 
show  halting  points  at  the  tem- 
perature of  transformation.  More- 
over, the  halting  periods  will  show 
a  maximum  at  the  concentration 
of  the  changing  variety,  and  a 
linear  decrease  from  this  value,  on 
both  sides,  toward  those  concen- 
trations wherein  the  quantity  of 
this  crystalline  variety  becomes 
zero.  The  diagram  given  in  Fig.  44 
represents  a  case  according  to  which 
two  substances  A  and  B  form  no 
compound  with  one  another,  but 
the  substance  A  sustains  polymor- 
phous transformation  from  the  /? 
form  into  the  a  form  (see  p.  11) 
at  a  temperature  t2,  located  below 

the  eutectic  temperature  tr  The  heat  of  transformation  liberated 
in  the  several  concentrations  is  represented  by  verticals  located 
upon  the  horizontal  cd,  and  decreases,  as  we  see,  from  concentra- 
tion 0  (pure  A),  where  the  maximum  value  obtains,  lineally  toward 
concentration  100  (pure  B),  where  the  zero  value  is  reached. 


Weight  per  cent  B 
FIG.  44. 


TWO  COMPONENT  SYSTEMS. 


145 


Let  us  now  turn  to  the  case  given  in  Fig.  45,  according  to 
which  two  substances  form  no  compound  on  being  fused  in  con- 
junction, but  separate,  on  cooling,  in  the  pure  state,  along  the 
respective  curve  branches  AC  and  BC.  At  the  temperature  t2, 
located  below  the  eutectic  temperature  tl}  however,  they  are 
assumed  to  enter  into  the  chemical  combination  AmBn,  the 
corresponding  reaction  being  ac- 
companied by  a  considerable  heat 
effect.  The  equation  describing  this 
complete  (per  assumption)  reaction, 
reads : 

mA  +  nB<=*AmBn. 

According  to  p.  32,  the  reaction 
takes  place  at  constant  tempera- 
ture. On  abstracting  heat,  the 
quantity  of  A  and  B  crystals  de- 
creases, while  the  quantity  of  AmBn 
crystals  increases,  without  change 
in  the  composition  of  any  phase;  in 
other  words,  complete  equilibrium 
obtains,  and  the  temperature  re- 
mains constant  until  reaction  ceases. 
On  supplying  heat,  reaction  pro- 
ceeds in  the  reverse  direction;  the 
compound  AmBn  decomposes  into  the  two  crystalline  varieties 
A  and  B  at  constant  temperature  (t2°).  Above  t2°,  the  crystalline 
varieties  A  and  B  are  stable  in  the  presence  of  one  another; 
below  t2°,  either  A  and  AmBn,  or  B  and  AmBn,  according  to  con- 
centration, are  mutually  stable. 

The  maximum  heat  effect  along  the  horizontal  cd  occurs  at  the 
concentration  of  the  compound  AmBn,  and  we  have  a  linear 
decrease  from  this  concentration  toward  pure  A  and  pure  B,  as 
shown  in  Fig.  45.  The  distinction  between  the  case  of  poly- 
morphous transformation  (shown  in  Fig.  44)  and  the  case  of 
chemical  combination  between  two  crystalline  varieties  with 
formation  of  a  third  (shown  in  Fig.  45)  may  now  be  drawn. 
Briefly,  it  lies  in  the  characteristic  location  of  the  maximum  heat 
effect,  in  the  first  case,  at  a  concentration  wherein  the  system  is 
composed  of  a  single  crystalline  variety,  and,  in  the  second  case, 


Weight  per  cent  B  \ 

AmBn 
FIG.  45. 


146 


THE   ELEMENTS   OF  METALLOGRAPHY. 


at  a  concentration  wherein  two  varieties  are  present  (in  the  pro- 
portions given  by  the  equation  of  the  reaction). 

If  a  compound  AmBn  sustains  polymorphous  transformation, 
as  many  additional  criteria  (supplementing  those  given  previously) 
are  thereupon  available  in  the  determination  of  its  composi- 
tion as  the  number  of  its  transformations.  The  case  according 
to  which  a  compound  AmBn,  melting  unchanged  at  C,  sus- 
tains two  transformations,  is  shown  in  Fig.  46.  One  of  these 
occurs  at  the  temperature  tlt  above  the  two  eutectic  tempera- 
tures, and  the  other  at  the  temperature  t4,  below  the  eutectic 


0  Weight  per  cent  [B 
AmBn 

FIG.  46. 


0  Weight  per  cent  B  100 

AmBn 

FIG.  47. 


temperatures.  We  note  that  the  positions  of  the  maxima  of 
halting  periods  along  the  two  horizontals  £t  and  t4  serve  as  inde- 
pendent expedients  relative  to  determination  of  the  composition 
of  the  compound,  since  these  maxima  must  occur  at  the  concen- 
tration of  the  pure  compound,  as  previously  pointed  out.  The 
fusion  curve  must  show  breaks  at  the  respective  points  F  and  G, 
and  the  dotted  continuations  of  the  curve  branches  into  the 
unstable  region  must  possess  the  positions,  relative  to  the  full 
curve  of  stable  equilibrium,  shown  in  the  figure,  owing  to  the 
lesser  solubility  of  the  stable  crystalline  variety  at  the  correspond-, 
ing  temperatures  (see  p.  110).  Pure  A  is  to  be  regarded  as  sol- 


TWO  COMPONENT  SYSTEMS.  147 

vent  at  F,  and  pure  B  at  G.  It  is  true,  however,  that  such  breaks 
frequently  escape  observation,  in  line  with  the  general  difficulty 
of  obtaining  an  exact  experimental  determination  of  the  fusion 
curve. 

Completely  analogous  relations  obtain  when  a  compound 
which  melts  under  decomposition  sustains  polymorphous  trans- 
formation. In  Fig.  47,  the  compound  AmBn  decomposes  into 
B  crystals  and  melt  of  concentration  E,  at  the  temperature  tr 
The  maxima  of  reaction  periods  along  the  horizontals  t2  and  t4, 
corresponding  to  polymorphous  transformations,  coincide  with 
the  concentration  of  the  compound  AmBn.  When  the  reaction 
between  crystalline  variety  B  and  melt  E  is  incomplete,  the  com- 
plications treated  on  p.  134  et  seq.  ensue. 

Under  normal  conditions,  obviously  that  crystalline  variety 
alone  which  is  stable  at  the  lowest  temperature  will  appear  in 
sections  of  the  reguli.  It  is,  nevertheless,  possible,  in  many 
instances,  to  hinder  the  processes  which  occur  in  the  crystallized 
alloys  by  very  rapid  cooling  (so-called  quenching),  and  to  transfer 
the  crystalline  varieties  which  are  stable  at  higher  temperatures 
into  a  region  of  lower  temperature  without  change,  notwithstand- 
ing their  instability  under  the  latter  condition.  Such  practice 
is  quite  analogous  to  that  of  obtaining  a  liquid  in  the  amor- 
phous-glassy form  (p.  9)  as  a  result  of  sudden  cooling,  regardless  of 
the  actual  stability  of  the  crystalline  form  at  the  lower  tempera- 
ture. Its  feasibility  rests  upon  the  invariable  decrease  in  reaction 
velocity,  and  of  crystallization  velocity,  with  falling  temperature. 

If  it  is  desired  to  examine  an  alloy,  the  components  A  and  B  of 
which  exhibit  the  relations  depicted  in  Fig.  45  (viz.,  unite  chemi- 
cally to  form  AmBn  at  the  temperature  t2)  at  ordinary  tempera- 
ture, in  the  condition  which  it  normally  assumes  between  the 
temperatures  ^  and  t2  —  a  condition  of  mixture  embracing  A,  B 
and  eutectic  —  it  will  be  necessary  to  rapidly  conduct  it  through 
the  temperature  range  wherein  the  rate  of  formation  of  AmBn  is 
at  all  rapid,  and  bring  it  into  a  temperature  region  where  this 
rate  is  practically  zero.  With  this  in  view,  the  alloy  is  quenched 
by  plunging  in  cold  water  as  soon  as  it  has  become  completely 
solidified,  i.e.,  when  the  temperature  has  fallen  below  tlt  but  not 
as  far  as  £,.  Under  these  conditions,  the  reaction  of  formation 
of  AmBn  frequently  fails  to  materialize  to  any  considerable  extent, 


148  THE  ELEMENTS  OF  METALLOGRAPHY. 

owing  to  the  rapidity  of  cooling  at  the  temperature  t2,  while, 
immediately  thereafter,  the  temperature  will  have  fallen  so  far 
below  t2  that  the  rate  of  reaction  will  have  become  practically 
zero.  Then  again,  the  once  cooled  alloy  may  be  subsequently 
heated  above  t2°,  in  order  to  decompose  the  quantity  of  com- 
pound which  was  originally  formed  on  slow  cooling,  and  there- 
upon quenched.  Obviously,  the  same  process  applies  where  a 
single  crystalline  variety  sustains  polymorphous  transformation, 
as  represented  in  Fig.  44.  Whether  or  not  the  quenching  process 
will  yield  satisfactory  results,  of  course  depends  upon  the  rela- 
tion between  rate  of  cooling  and  rate  of  reaction  for  the  respec- 
tive change.  If  the  rate  of  reaction  at  t2  is  unusually  rapid,  it 
will  scarcely  be  possible  to  secure  sufficiently  rapid  cooling  to 
restrain  the  process.  In  practice,  cases  in  which  quenching  is 
quite  futile,  on  account  of  excessive  rate  of  reaction,  are  encoun- 
tered, as  well  as  those  in  which  the  result  is  entirely  satisfactory, 
viz.,  in  which  the  reaction  is  practically  eliminated  by  proper 
quenching.  Between  these  two  extremes,  we  find  instances  in 
which  a  greater  or  lesser  portion  of  the  crystalline  varieties  stable 
at  higher  temperatures  may  be  safely  transferred  into  the  region 
of  ordinary  temperature. 

Finally,  attention  may  be  drawn  to  the  fact  that  the  rule  plac- 
ing the  number  of  compounds  equal  to  the  number  of  branches 
of  the  fusion  curve  diminished  by  two,  fails  to  hold  when  changes 
occur  in  the  crystalline  state.  In  Fig.  45,  the  fusion  curve  is 
composed  of  two  branches  only,  and  yet  a  compound  AmBn 
exists.  In  Fig.  46,  there  are  four  points  D,  F,  G  and  E  of  the 
fusion  curve  which  correspond  to  abrupt  change  in  its  direction. 
Thus,  there  are  five  branches,  although  no  more  than  one  com- 
pound (AmBn)  exists. 

In  consideration  of  the  many  horizontals  of  constant  tempera- 
ture which  traverse  the  diagram  where  polymorphous  transfor- 
mation occurs,  it  appears  that  the  rule  placing  the  number  of 
compounds  equal  to  the  number  of  eutectic  horizontals  dimin- 
ished by  one,  is  robbed  of  all  practical  significance.  It  may  be 
retained,  to  be  sure,  if  the  horizontals  arising  from  polymor- 
phous transformation  be  excluded  from  the  enumeration.  Dif- 
ferentiation between  the  individual  horizontals,  however,  cannot 
be  attempted  unless  knowledge  of  the  whole  diagram  is  at  hand. 


TWO  COMPONENT  SYSTEMS.  149 

§  2.  THE  LIQUID  STATE  is  CHARACTERIZED  BY  INCOMPLETE  Mis- 
CIBILITY;  THE  CRYSTALLINE  STATE  BY  COMPLETE  IMMIS- 
CIBILITY. 

We  have  observed  on  p.  37  that  the  case  of  complete  immis- 
cibility  of  two  pure  substances  is  to  be  regarded  theoretically  as 
a  limiting  case  of  extremely  slight  miscibility.  When  we  bring 
two  liquid  substances  A  and  B  into  close  association  at  a  tem- 
perature ^  where  they  fail  to  mix  completely  with  one  another, 
and  take  care  that  they  reach  equilibrium,  by  means  of  stirring 
or  shaking,  each  will  become  saturated  with  the  other.  If,  now, 
the  system  be  left  to  itself,  the  two  solutions  will  separate  after 
standing  a  sufficient  length  of  time,  by  reason  of  their  varying 
specific  weight,  and  two  layers  will  result.  One  of  these  con- 
sists of  A,  saturated  with  B;  the  other  of  B,  saturated  with  A. 
We  characterize  the  A -richer  layer  as  solution  of  B  in  A,  and 
the  5-richer  layer  as  solution  of  A  in  B.  The  respective  concen- 
trations of  the  two  saturated  solutions  at  the  given  temperature 
may  be  ascertained  by  quantitative  analysis.  Now,  in  general, 
the  solubility  of  substances  in  one  another  increases  with  the 
temperature.  We  will  therefore  assume  this  to  be  the  case  rela- 
tive to  molten  metals  when  dissolved  in  one  another.  If,  then, 
the  composition  of  two  layers  which  have  reached  equilibrium 
at  some  higher  temperature  t2  be  investigated,  we  shall  find  that 
the  solution  of  B  in  A  has  become  5-richer,  and  the  solution  of 
A  in  B,  A-richer. 

A  concentration-temperature  diagram  is  again  used  to  bring 
out  these  relations  (Fig.  48).  The  point  at  corresponds  to  a 
saturated  solution  of  B  in  A  at  the  temperature  tlt  and  the  point  6t 
to  a  saturated  solution  of  A  in  B  at  the  same  temperature.  The 
corresponding  points  for  a  temperature  t2  are  a2  and  62;  they  must 
be  nearer  together  than  the  first  points,  as  explained  above.  On 
proceeding  with  the  determination  of  composition  of  the  satu- 
rated solutions  for  higher  temperatures,  we  continually  obtain 
closer  values  until,  at  length,  coincidence  results  (at  the  point  c) 
—  unless  the  mixture  commences  to  boil  at  some  lower  tempera- 
ture. 

The  saturated  solution  of  B  in  A  then  possesses  the  same  com- 
position as  the  saturated  solution  of  A  in  B,  i.e.,  both  solutions 


150 


THE  ELEMENTS  OF  METALLOGRAPHY. 


are  identical  at  this  and  all  higher  temperatures.  Thus,  the 
mixture  can  no  longer  separate  into  two  layers;  we  have  reached 
the  region  of  complete  miscibility.  By  passing  a  continuous 
curve  through  the  experimentally  determined  points,  we  obtain 
the  solubility  curve,  which  supplies  exhaustive  information  rela- 
tive to  all  questions  concerning  this  particular  phenomenon. 


Weight  per  cent  B 
FIG.  48. 


100 


In  the  region  situated  without  the  solubility  curve,  the  system 
is  homogeneous,  while  within  the  solubility  curve  the  system  is 
composed  of  two  layers.  Assuming  that  a  given  system  is 
defined  as  to  concentration  and  temperature  by  the  point  x,  the 
points  of  intersection  y  and  z  of  the  solubility  curve  with  a  hori- 
zontal passing  through  x  define  the  composition  of  the  two 
layers  which  are  in  equilibrium  at  the  temperature  corresponding 
to  x.  Thus,  the  system  x  must  have  separated  into  layers  of  the 
respective  concentrations  y  and  z,  and  the  relative  quantities  of 
y  and  z  may  be  determined  in  the  usual  manner,  according  to 
the  lever  relation. 

(Quantity  y)  •  xy  =  (Quantity  z)  •  xz. 

In  spite  of  the  fact  that  limited  miscibility  in  the  molten  state 
is  by  no  means  rare  among  the  metals,  solubility  curves  are  avail- 
able in  case  of  two  pairs  only,  namely,  lead-zinc  and  bismuth- 


TWO  COMPONENT  SYSTEMS.  151 

zinc.  The  first  of  these  pairs  is  of  some  interest  in  the  arts  (see 
p.  37).  Previous  investigation  has  been  for  the  most  part  confined 
to  the  behavior  of  transparent  liquids  at  rather  low  temperatures. 
In  such  cases,  the  method  of  ALEXEJEW*  constitutes  a  very  simple 
procedure  for  determining  the  points  of  the  solubility  curve. 
Mixtures  of  known  concentration  are  prepared  by  weighing,  and 
the  temperature  at  which  the  cooling  liquid  begins  to  separate  is 
observed.  The  resulting  turbidity  may  be  sharply  recognized. 
We  note  that  by  this  method  no  determination  of  the  points  of 
intersection  y  and  z  of  the  constant  temperature  horizontal  with 
the  solubility  curve  is  effected  (this  would  require  separation  and 
analysis  of  the  two  layers);  it  is  the  point  of  intersection  v  of  a 
definite  concentration  vertical  with  the  solubility  curve  which  is 
hereby  located  (requiring  only  one  temperature  observation, 
since  a  weighed  quantity  of  material  is  used  at  the  start).  A  proc- 
ess of  this  sort  is  obviously  inapplicable  to  opaque  substances 
(metals).  The  substitution  of  an  analogous  method,  prescribing 
thermal  determination  of  the  initial  temperature  of  separation, 
might  seem  well  advised  in  connection  with  metallic  mixtures. 
Unfortunately,  however,  the  heat  effect  attending  separation  is 
too  small  for  this  purpose. 

On  separation  of  the  homogeneous  liquid  into  two  layers,  a  certain 
quantity  of  heat  must  be  liberated,  if  our  assumption  that  the  miscibility 
increases  with  rising  temperature  is  correct.  Otherwise,  our  system 
could  not  be  stable  in  the  form  of  two  layers.  This  will  be  understood 
from  the  following  considerations:  If  the  separation  which  occurs  on 
cooling  were  attended  by  heat  absorption,  the  reverse  process  of  mixture 
on  heating  would  of  necessity  be  attended  by  liberation  of  heat.  Thus, 
if  the  system  composed  of  two  layers  in  equilibrium  were  existent  at  a 
certain  temperature  tl}  the  slightest  elevation  of  temperature  would 
increase  the  miscibility.  Since  heat  would  be  liberated  during  the 
ensuing  mixture,  further  elevation  of  temperature,  and,  therefore,  further 
increase  in  miscibility,  would  be  inevitable.  The  same  process  would 
thereupon  repeat  itself,  and  become  progressive,  whereby  a  homogene- 
ous mixture  would  be  ultimately  produced.  Thus,  the  original  system  of 
two  layers  would  have  been  unstable.  Hence,  for  stability  when  misci- 
bility increases  with  rising  temperature  or,  what  amounts  to  the  same, 
when  separation  occurs  with  falling  temperature,  this  latter  process  must 
be  accompanied  by  liberation  of  heat.  The  above  reasoning  is  of  general 

1  ALEXEJEW,  Wied.  Ann.,  28,  305  (1886). 


152  THE  ELEMENTS  OF  METALLOGRAPHY. 

application.  An  assumption  of  equilibrium  in  a  system  is  equivalent  to 
a  concession  that  heat  addition  can  effect  such  changes  only  as  are 
attended  by  heat  absorption.  If,  for  example,  we  add  heat  to  a  crystal 
which  is  in  equilibrium  with  its  melt,  it  is  justifiable  to  conclude  from  the 
ensuing  fusion  that  this  process  must  be  attended  by  heat  consumption. 
For,  if  the  fusion  were  attended  by  evolution  of  heat,  the  slightest  addi- 
tion of  heat  would  suffice  to  effect  complete  fusion,  with  spontaneous 
rise  in  temperature,  —  progressive  fusion,  even  though  inappreciable  in 
its  individual  stages,  would  represent  an  ever-increasing  source  of  further 
heat  evolution.  The  same  statements  hold  in  the  case  of  transformation 
from  an  a  form  into  the  corresponding  /?  form  (see  p.  11).  We  are  at 
liberty  to  conclude  with  equal  right  that  the  reaction, 

AmBn  «=>  mA  +  nB  (p.  145), 

which  proceeds  from  left  to  right  on  addition  of  heat,  is  attended  by 
heat  absorption,  and  that,  in  proceeding  in  the  reverse  direction  on 
cooling,  is  attended  by  heat  evolution.  As  long  as  we  are  dealing  with 
equilibrium  conditions,  any  process  which  occurs  on  cooling  is  accordingly 
attended  by  heat  evolution. 

Van't  Hoff's  Principle  as  above,  which,  in  association  with  an  anal- 
ogous principle  relating  to  the  effect  of  pressure  upon  displacement  of 
equilibrium,  is  commonly  designated  as  LeChatelier's  Principle,  places  no 
limit  upon  the  magnitude  of  the  heat  effect.  It  may  be  indefinitely 
small.  As  a  matter  of  fact,  the  heat  quantity  liberated  during  separa- 
tion of  a  homogeneous  liquid  into  two  layers  is  so  slight  that  it  causes  no 
noticeable  break  upon  the  cooling  curves  (see  above). 

Separation  of  the  two  layers  at  the  temperatures  for  which 
points  of  the  solubility  curve  are  to  be  determined  therefore  con- 
stitutes the  sole  remaining  expedient  relative  to  determination  of 
the  solubility  curve  of  two  fused  metals.  The  experimental  diffi- 
culty associated  with  work  of  this  sort  is  responsible  for  our 
insufficient  knowledge  of  the  prevailing  conditions  in  such  cases. 
SPRING  and  ROMANOFF/  to  whom  we  are  indebted  for  investiga- 
tion of  the  metal  pairs,  lead-zinc  and  bismuth-zinc,  used  crucibles 
of  clay  mixed  with  graphite,  the  side  walls  of  which  contained 
at  a  certain  elevation,  an  aperture  which  was  closed  by  a  plug 
of  the  same  material.  They  were  filled  in  such  a  manner  that 
the  dividing  line  of  the  two  layers  was  situated  at  the  opening, 
after  occurrence  of  equilibrium.  The  mixture  was  heated  to 
1  SPRING  and  ROMANOFF,  Z.  anorg.  Chem.,  13,  29  (1896). 


TWO  COMPONENT  SYSTEMS. 


153 


the  temperature  of  investigation,  stirred,  and  then  left  to  stand. 
A  sample  from  the  upper  layer  was  at  length  obtained  by  means 
of  a  spoon.  Ultimately,  the  plug  was  removed  from  the  open- 
ing with  the  aid  of  an  iron  rod,  and  the  upper  layer  allowed  to 
flow  off,  whereby  its  separation  from  the  lower  layer  was  effected. 
The  results  of  these  authors  certify  to  increasing  solubility  of  the 
two  substances  in  one  another  with  rising  temperature,  and  also 
show  agreement  with  the  conditions  represented  in  Fig.  48  in  all 
other  respects. 

We  may  now  proceed  to  study  the  fusion  diagram  as  it  appears 
in  several  special  cases  under  the  above  heading. 

A.    The  Components  do  not  Unite  to  Form  a  Chemical  Compound. 

Two  elements  A  and  B  possessing  the  melting  points  A  and  B 
(Fig.  49)  are  now  to  be  considered.     Let  DFE  represent  the  solu- 


W eight  jper  v&aJL  JB 
FIG.  49. 


100 


bility  curve  of  the  two  melts.  This  is  given  by  a  dotted  line, 
since  the  very  inconsiderable  heat  of  separation  of  the  two 
liquid  layers  precludes  its  determination  thermally.  Then,  in  the 
region  outside  of  the  curve  DFE,  we  have  liquid  alloy  consisting 


154  THE  ELEMENTS   OF  METALLOGRAPHY. 

of  a  single  layer:  complete  miscibility  in  the  liquid  state,  and  in 
the  crystalline  state  as  well  according  to  previous  assumption, 
obtains  here.  The  law  of  freezing-point  depression  must  there- 
fore hold  in  this  case,  whence  the  melting  point  of  A  is  lowered 
along  the  curve  branch  AC  by  addition  of  B,  and  the  melting 
point  of  B  along  the  curve  branch  BE  by  addition  of  A  (cf.  p.  38). 

Now,  one  of  these  curve  branches  will  intersect  the  solubility 
curve  DFE  at  the  higher  temperature,  namely,  the  branch  BE  at 
E,  corresponding  to  the  temperature  Jr  It  may  thereupon  be 
shown  that  the  solubility  curve  no  longer  represents  stable  con- 
ditions below  the  temperature  tlt  since  a  solution  of  concentra- 
tion E  is  the  solution  of  A  in  B  which  is  stable  at  the  lowest  tem- 
perature. (Those  solutions  situated  upon  the  B-rich  side  are 
called  solutions  of  A  in  B,  and  those  upon  the  A-rich  side,  solu- 
tions of  B  in  A.)  This  follows  from  the  fact  that  E  represents  a 
point  of  the  solubility  curve  DFE  and  of  the  fusion  curve  BE  as 
well.  Alloys  of  such  concentrations  as  are  located  between  E 
and  100  (pure  B)  change  on  cooling  to  a  solution  of  concentra- 
tion E  through  separation  of  pure  B;  those  of  concentrations 
between  D  and  E  produce  the  same  solution  through  separation 
of  a  second  liquid  layer,  of  concentration  D.  This  solution  is 
therefore  saturated  with  both  A  and  B. 

The  conditions  which  we  have  here  are  similar  to  those  pertain- 
ing to  eutectic  crystallization,  wherein  a  melt  is  also  saturated 
with  two  substances,  and  separation  of  one  determines  simulta- 
neous separation  of  the  other.  But  here,  the  A  material,  instead 
of  separating  in  the  form  of  pure  crystals,  assumes  the  form  in 
which  it  is  in  equilibrium  with  the  melt  E}  viz.,  it  occurs  as  sat- 
urated solution  of  B  in  A,  corresponding  to  concentration  D  at 
this  temperature.  Consequently,  at  the  temperature  $,,  crystal- 
line- B  is  in  equilibrium  with  two  melts,  of  the  respective  con- 
centrations D  and  E.  (That  crystalline  B  is  in  equilibrium  with 
the  melt  D  as  well,  follows  from  the  principle  enunciated  on 
p.  27,  according  to  which  a  given  equilibrium  is  independent  of 
the  arrangement  of  the  several  phases.)  If  the  melt  E  sepa- 
rates an  additional  quantity  of  crystalline  B}  a  definite  amount 
of  melt  D,  determined  by  its  A-content,  must  simultaneously 
appear.  Thus,  the  equation  of  the  reaction  reads: 
Melt  E  «=*  Crystalline  variety  B  +  Melt  D. 


TWO  COMPONENT  SYSTEMS.  155 

On  cooling,  melt  of  composition  E  disappears,  while  the  quan- 
tity of  B  crystals,  and  of  melt  of  composition  D,  increases,  with- 
out change  in  the  composition  of  any  phase,  i.e.,  we  are  dealing 
with  a  condition  of  complete  equilibrium,  and  the  temperature 
must  remain  constant  until  one  phase  becomes  exhausted  —  on 
cooling,  this  is  the  melt  E.  No  fall  of  temperature  can  ensue,  on 
continued  cooling,  until  all  E  is  exhausted  and  only  melt  D  and 
crystalline  B  remain.  When  the  temperature  has  finally  fallen 
below  tlt  however,  further  separation  of  B  must  occur  in  the  form 
of  B  crystals,  not  as  solution  of  A  in  B,  since  such  a  solution  is 
no  longer  stable  below  this  temperature:  indeed,  the  only  B-rich 
solution  which  could  exist  at  the  temperature  ^  would  have 
become  completely  exhausted  by  the  time  this  temperature  had 
been  reached.  A  single  type  of  solutions,  namely,  the  A-rich 
solutions,  of  concentrations  from  D  to  0  (=  pure  A),  are  capable 
of  existence  below  t°.  We  have  designated  these  as  solutions 
of  B  in  A.  Thus  it  is  clear  that  the  stable  portion  of  the  solu- 
bility curve  DFE  ends  at  the  points  D  and  E  of  temperature 
£j.  Since  we  have  again  reached  the  region  of  complete  misci- 
bility  in  the  liquid  state  in  concentrations  from  D  to  0  (=  pure  A), 
it  is  at  once  seen  that  further  separation  of  B  is  attended  by  fall- 
ing temperature  and  enrichment  of  the  melt  in  A  along  the  curve 
branch  D(7.  Eutectic  crystallization  occurs  at  the  point  C, 
representing  intersection  of  the  curve  branches  DC  and  AC 
(temperature  t2).  Crystallization  of  the  various  melts  proceeds 
as  follows: 

(1)  Separation  of  crystalline  B  follows  the  branch  BE  in  all 
concentrations  which  are  located  between  100  (=  pure  B)  and 
E,  having  commenced  at  that  point  of  this  branch  which  cor- 
responds to  the  concentration  in  question.  The  melt  increases  its 
A-content,  through  separation  of  B,  until  the  temperature  tt  is 
reached  at  concentration  E.  Continued  crystallization  of  B 
occurs  at  this  constant  temperature,  accompanied  by  separation 
of  a  second  liquid  layer  of  composition  D,  containing  the  excess 
of  A.  The  period  of  constant  temperature  lasts  until  no  melt  E 
remains  in  presence  of  B  crystals  and  melt.  Further  separation  of 
B  then  ensues  along  the  branch  DC,  whereby  the  temperature 
falls,  and  the  melt  becomes  richer  in  A  up  to  the  concentration 
C.  The  remainder  of  melt  (of  concentration  C)  then  crystallizes 


156  THE  ELEMENTS   OF   METALLOGRAPHY. 

at  constant  temperature  to  an  eutectic  composed  of  B  and  A. 
Cooling  curves  therefore  show  breaks  at  the  time  of  passing  the 
curve  branch  BE,  halting  points  at  If,  and  halting  points  at  t2°. 

(2)  The  cooling  curve  of  a  melt  of  concentration  E  shows  no 
break  to  correspond  with  the  curve  branch  BE,  but  merely  the 
two  halting  points  at  t°  and  t2°,  respectively. 

(3)  The  same  is  true  of  the  cooling  curves  which  correspond 
to  concentrations  from  D  to  E,  since  the  heat  effect  due  to  separa- 
tion of  the  melt  into  two  layers  on  traversing  the  solubility  curve 
DFE  is  so  slight  as  to  escape  observation. 

(4)  The  cooling  curves  of  concentrations  located  between  D  and 
C  no  longer  show  halting  points  at  t°.     On  the  contrary,  primary 
crystallization  of  B  sets  in  at  that  point  of  the  curve  branch  DC 
which  corresponds  to  the  respective  concentration,  without  pre- 
vious separation  of  the  melt  into  two  liquid  layers.     Such  crys- 
tallization continues  along  DC  up  to  the  point  D,  when  the 
remainder  of  the  melt  solidifies  eutectically.     Thus,  the  cooling 
curves  show  breaks  below  t°,  and  halting  points  at  t2°. 

(5)  A  melt  of  concentration  C  solidifies  eutectically.     Its  cool- 
ing curve  therefore  shows  a  single  halting  point  at  t2°. 

(6)  Alloys  of  concentrations  from  0  (=  pure  A)  to  C  separate 
crystalline  A  primarily  along  the  curve  branch  AC  and  also  com- 
plete their  solidification  eutectically  at  C.     Hence  their  cooling 
curves  show  breaks,  followed  by  halting  points  at  t2°.     As  we  have 
seen,  the  following  process  takes  place  at  the  constant  tempera- 
ture tj_ : 

Melt  E  <=*  Crystalline  variety  B  +  Melt  D. 

Thus,  the  heat  quantity  liberated  during  the  change,  and,  under 
the  customary  assumptions,  the  length  of  the  halting  point  at  tf 
as  well,  is  given  by  the  relative  quantity  of  melt  E  present 
at  this  temperature.  The  maximum  value  1  of  these  halting 
periods  at  t£  is  reached  at  concentration  E.  From  E,  this  value 
decreases  lineally  toward  concentrations  D  and  100  (  =  pure  J5), 
where  the  zero  value  obtains. 

Similarly,  the  relative  quantity  of  eutectic  attains  its  maximum 
at  concentration  C  and  decreases  lineally  toward  concentrations 
0  (=  pure  A)  and  100  (=  pure  B),  where  zero  is  reached. 

This  is  depicted  in  Fig.  49,  according  to  the  usual  practice,  by 
erection  of  verticals  along  the  horizontals  DEc  and  aCb. 


TWO  COMPONENT  SYSTEMS. 


157 


It  is  characteristic  of  this  diagram  that  two  constant  temper- 
ature horizontals  are  present,  notwithstanding  the  entire  absence 
of  compounds  and  polymorphous  transformations.  The  non- 
existence  of  a  compound  is  determined  by  the  fact  that  the 
eutectic  horizontal  aCb  extends  throughout  the  whole  diagram, 
and  that  the  relative  quantity  of  eutectic  decreases  lineally  from 
the  eutectic  concentration  toward  both  sides. 

As  to  the  fields  of  condition,  we  note  that  the  region  of  melt 
above  AC  DEB  is  divided  into  two  portions: 

(1)  The  field  of  homogeneous  melt  above  ACDFEB,  and 

(2)  The  field  of  two  liquid  layers,  bounded  by  the  solubility 
curve  DFE  and  the  horizontal  DE. 


Weight  per  cent  B 
FIG.  50. 

Furthermore,  we  have  two  fields  with  one  crystalline  variety, 
namely : 

(1)  The  field  BEDCb  of  B  crystals  and  melt,  the  latter  generally 
consisting  of  two  layers  along  the  horizontal  DEc,  and 

(2)  The  field  ACa  of  A  crystals  and  melt. 

The  two  fields  with  two  crystalline  varieties  are: 
(1)  bCdf,  corresponding  to  primarily  separated  B  crystals  and 
eutectic  C,  and 


158 


THE  ELEMENTS   OF  METALLOGRAPHY. 


(2)  aCde,  corresponding  to  primarily  separated  A  crystals  and 
eutectic  C. 

The  partial  miscibility  of  A  and  B  in  the  vicinity  of  the  melting 
point  of  the  least  fusible  component  may  differ  considerably  in 
extent.  It  is  assumed  to  be  inconsiderable  in  Fig.  50,  i.e.,  the 
compositions  of  the  two  layers  differ  only  slightly  from  those  of 
the  respective  pure  substances  at  the  melting  point  of  B.  On 
this  account,  the  point  E  falls  only  a  trifle  below  B,  in  that  the 
curve  branch  of  primary  B  separation  meets  the  solubility  curve 
soon  after  leaving  B.  Thus,  the  temperature  ^  of  the  horizontal 


D 


Weight  per  cent  B 
FIG.  51. 


100 


cED  is  very  little  lower  than  the  melting  point  of  B.  The  same 
holds  relative  to  the  temperature  t2  of  the  eutectic  horizontal 
aCb  —  this  temperature  lies  very  little  below  the  melting  point 
of  pure  A.  The  limiting  case  in  which  both  substances  fail 
entirely  to  dissolve  in  one  another  in  the  liquid  state  at  the  melt- 
ing point  of  B,  viz.,  in  which  both  layers  represent  pure  sub- 
stances, is  shown  in  Fig.  51.  Here,  the  point  E  coincides  with  B, 
and  the  point  C  with  A.  All  concentrations,  with  exception  of 
the  pure  substances,  give  cooling  curves  with  two  halting  points, 
^  and  t2,  corresponding  to  the  melting  points*of  the  pure  metals. 


TWO  COMPONENT  SYSTEMS.  159 

It  is  then  evident  that,  although  thermal  analysis  yields  no 
information  concerning  the  course  of  the  solubility  curve  of  the 
two  melts,  it  does  fix  the  two  lowest  points  D  and  E  of  this  curve. 

Concerning  the  structure  of  the  sections,  we  infer  that,  provided 
the  two  substances  are  rather  soluble  in  one  another,  as  was 
assumed  in  the  construction  of  Fig.  49,  the  present  conditions 
practically  duplicate  those  presented  by  the  case  of  complete 
miscibility  in  the  liquid  state,  unaccompanied  by  chemical  com- 
bination (Fig.  lla).  For,  we  have  in  this  case  as  well,  primarily 
separated  A  or  B,  according  to  concentration,  surrounded  by 
eutectic.  However,  primary  separation  of  the  crystalline  variety 
B  from  concentrations  between  100  per  cent  B  and  D  will  have 
occurred  in  the  B-rich  layer  alone,  during  the  first  stage.  Not 
until  this  layer  has  disappeared,  does  the  D  layer  begin  to  crystal- 
lize —  yielding  B,  and  subsequently  eutectic.  It  is  often  possible 
to  determine  from  the  appearance  of  the  section  under  the  micro- 
scope that  crystallization  has  taken  place  in  two  layers.  In 
general,  the  layers  become  more  distinct  as  mutual  solubility  in 
the  liquid  state  decreases.  At  times,  however,  when  the  specific 
weights  of  A  and  B  are  not  widely  different,  separation  into  two 
layers  fails  to  show,  even  in  cases  of  slight  miscibility.  In  such 
cases,  the  two  solutions  will  not  have  separated  sharply,  but 
will  have  formed  an  emulsion  —  one  layer  impregnating  the  other 
in  the  form  of  minute  drops  —  at  the  beginning  of  crystalliza- 
tion. These  characteristic  enclosures  are  easily  recognized  under 
the  microscope. 

The  systems  Na-Al1  and  T1-A12  may  be  cited  as  examples  of 
practically  complete  immiscibility  in  the  liquid  state.  Mutual 
solubility  of  the  components  at  the  temperature  of  initial  crystal- 
lization is  quite  appreciable  in  the  systems  Na-Mg,3  Al-Bi4  and 
Zn-Tl.5  In  the  system  Tl-Cu,6  molten  copper  is  capable  of  dis- 
solving some  35  per  cent  of  thallium  at  the  temperature  of  its 
melting  point  (1084  degrees),  while  molten  thallium  will  dissolve 
some  2  per  cent  of  copper  only  at  this  temperature.  Further 

1  MATHEWSON,  Z.  anorg.  Chem.,  48,  191  (1906). 
3  DOERINCKEL,  Z.  anorg.  Chem.,  48,  185  (1906). 

3  MATHEWSON,  L  c. 

4  GWYER,  Z.  anorg.  Chem.,  49,  311  (1906). 

6  v.  VEGESACK,  Z.  anorg.  Chem.,  52,  32  (1907). 
8  DOERINCKEL,  L  c. 


160 


THE  ELEMENTS  OF  METALLOGRAPHY. 


discussion  of  these  examples  appears  unnecessary:  bare  mention 
of  the  fact  that  examples  of  the  cases  represented  in  Figs.  49,  50 
and  51  are  actually  known,  as  above,  may,  indeed,  be  deemed 
sufficient. 

B.    The  Components  Unite  to  Form  a  Chemical  Compound. 

Obviously,  nothing  new  would  be  introduced  by  assuming, 
relative  to  Fig.  49,  that  one  of  the  components  of  the  system,  B, 
for  example,  were  a  compound  AmBn  instead  of  an  element.  As 
a  matter  of  fact,  we  observed  on  p.  77,  where  the  first  considera- 
tion of  changes  in  the  fusion  diagram  due  to  presence  of  a  com- 
pound was  entered,  how  a  fusion  diagram  may  be  divided  at  the 


Weight  per  cent  B 


AmBn 


FIG.  52. 


concentration  of  a  compound  which  melts  unchanged,  and  the 
separate  parts  regarded  as  individual  diagrams.  In  view  of  these 
considerations,  the  diagram  presented  in  Fig.  52  requires  no 
especial  explanation.  The  dotted  vertical  at  the  concentration  of 
the  compound  AmBn  divides  the  diagram  into  two  separate  dia- 
grams. Incomplete  miscibility  in  the  liquid  state  prevails  at  the 
left  of  this  line;  complete  miscibility  at  the  right.  The  com- 
pound AmBn  fuses  unchanged,  although  no  difficulty  would  be 


TWO  COMPONENT  SYSTEMS. 


161 


encountered  if  it  were  replaced  by  a  compound  melting  under 
decomposition  (" concealed  maximum"). 

The  diagrammatic  relations  which  obtain  when  the  composi- 
tion of  the  compound  lies  between  concentrations  D  and  E  are 
not  apparent  without  some  further  consideration.  The  compound 


Weight  per  cent  B 

FIG.  53. 


100 


will  not  melt  to  a  homogeneous  liquid,  but  must  separate  into  a 
mixture  (emulsion)  of  two  liquids.  Fig.  53  represents  the  fusion 
diagram  for  this  case. 

The  equation  of  the  reaction  reads: 

AmBn  <±  Melt  D  +  Melt  E, 

and  it  indicates  that  complete  equilibrium  is  at  hand,  whence 
the  process  must  take  place  at  constant  temperature  ft).  When 
the  compound  decomposes  on  heating,  the  quantity  of  both  melts 
increases,  and  the  quantity  of  AmBn  crystals  decreases.  The 
reverse  effect  ensues  on  re-formation  of  the  compound  as  heat  is 
abstracted.  No  phase  changes  its  composition. 

The  relative  quantity  of  AmBn  which  melts  at  the  temperature. 
tlf  with  formation  of  two  liquid  layers,  is  largest  at  the  concen- 
tration of  the  compound,  and  is  zero  at  concentrations  D  and  E. 


162  THE  ELEMENTS  OF  METALLOGRAPHY. 

This  is  shown  as  usual  in  the  diagram.  In  other  respects,  the 
present  diagram  is  not  fundamentally  different  from  that  shown 
in  Fig.  16c,  p.  78,  representing  the  ordinary  case  of  a  compound 
which  melts  without  decomposition.  The  earlier  case  may  be 
derived  from  the  present  case  by  shortening  the  horizontal  DE 
(Fig.  53)  until  it  finally  becomes  contracted  to  a  single  point, 
which  then  coincides  with  the  maximum  of  the  fusion  curve  of 
Fig.  16c.  The  solubility  curve  of  the  two  liquid  layers  has  now 
disappeared. 

Determination  of  the  maximum  of  reaction  periods  along  the 
horizontal  DE  serves  as  a  criterion  for  the  composition  of  the 
compound.  This  expedient  replaces  determination  of  the  maxi- 
mum along  the  fusion  curve  for  the  case  of  a  compound  which 
melts  to  a  homogeneous  liquid. 

A  single  example  of  this  case  is  to  be  found  in  the  literature. 
According  to  MATHEWSON/  sodium  and  zinc  unite  to  form  a 
Zn-rich  compound  (possibly  NaZnu  or  NaZn12)  which  melts  at 
557  degrees  to  a  liquid  composed  of  two  layers,  one  consisting  of 
practically  pure  sodium,  and  the  other  Zn-richer  than  the  com- 
pound.2 

§  3.    BOTH  THE  LIQUID  AND  CRYSTALLINE  STATES  ARE  CHARAC- 
TERIZED BY  COMPLETE  MISCIBILITY. 

We  have  already  noted  (p.  37)  that  it  is  by  no  means  a  rare 
occurrence  for  substances  to  dissolve  in  one  another  in  the  crys- 
talline state.  Indeed,  the  formation  of  mixed  crystals  is  very 
often  observed  in  the  case  of  metals.  On  this  account,  investiga- 
tion of  the  nature  of  metallic  alloys  is  subject  to  increased  diffi- 
culty. Now,  it  is  precisely  the  alloys  of  predominant  importance 
in  the  industries  —  Iron-Carbon  alloys,  the  Bronzes,  Brasses,  etc., 
—  whose  components  show  miscibility  in  the  crystalline  state, 
and  it  is  largely  owing  to  this  condition  that,  in  spite  of  the  many 
exact  investigations  which  have  been  devoted  to  these  systems, 
various  problems  still  await  solution. 

We  will  make  the  assumption  in  this  paragraph  that  the  two 

1  MATHEWSON,  Z.  anorg.  Chem.,  48,  191  (1906). 

2  SMITH,  Z.  anorg.  Chem.,  56,  119  (1907),  has  recently  observed  similar 
conditions  in  the  K-Zn  System.     The  compound,  in  this  case,  is  also  Zn-rich, 
corresponding  to  some  formula  approximating  K-Zn12. 


TWO  COMPONENT  SYSTEMS.  163 

metals  A  and  B  are  miscible  in  the  crystalline,  as  well  as  the  liquid, 
state  in  all  proportions.  In  such  a  case,  considerable  analogy  is 
to  be  noted  relative  to  the  respective  behavior  of  the  crystalline 
and  liquid  phases.  The  assumption  of  complete  miscibility  in 
the  liquid  state  denotes  that  homogeneous  melts  of  all  concentra- 
tions between  0  per  cent  B  and  100  per  cent  B  (pure  A  to  pure  B) 
may  be  prepared,  and  that  the  properties  of  these  melts  will 
vary  continuously  with  the  concentration.  The  same  is  true 
relative  to  the  case  of  complete  miscibility  in  the  crystalline  con- 
dition —  frequently  designated  as  the  case  of  complete,  or  un- 
broken, isomorphism.  VAN'T  HOFF  has  given  expression  to  the 
analogy  between  mixed  crystals  and  liquid  mixtures,  which 
appears  to  be  very  close  in  many  instances,  by  introduction  of 
the  term  "solid  solution."  l 

Complete  miscibility  in  the  liquid  and  crystalline  states  requires 
that  the  crystals  which  are  in  equilibrium  with  the  melt  be  alike 
in  composition  among  themselves.  It  is  quite  as  contrary  to  our 
original  assumption  for  the  crystals  which  are  in  equilibrium 
with  the  melt  to  be  of  different  varieties  (e.g.,  as  is  the  case  rela- 
tive to  crystallization  of  an  eutectic),  as  it  is  for  the  melt  to  sep- 
arate into  two  layers.  If  the  crystals  were  of  different  varieties, 
equilibrium  corresponding  to  complete  miscibility  in  the  crystal- 
line state  could  no  longer  be  in  evidence.  Let  us  imagine,  for 
example,  that  two  liquids  which  are  miscible  in  all  proportions, 
such  as  water  and  alcohol,  be  arranged  in  layers.  Then  the 
system  cannot  come  to  rest,  viz.,  equilibrium  cannot  result, 
until  the  two  liquid  layers  have  attained  the  same  concentration 
as  a  result  of  diffusion.  Precisely  the  same  conditions  obtain 
when  two  crystals  which  are  miscible  in  all  proportions  are 
brought  in  contact.  According  to  the  principle  that  equilibrium 
is  independent  of  the  arrangement  of  the  separate  phases  (see 
p.  27),  direct  contact  of  both  crystalline  varieties  is  not  essen- 
tial, for  equalization  of  concentration  may  be  attained  through 
the  medium  of  melt,  which  is  itself  in  contact  with  both  varieties. 
We  thus  conclude  that,  if  the  miscibility  is  complete  in  both  the 
liquid  and  crystalline  phases,  the  system,  in  order  to  be  in  equi- 
librium, must  comprise  only  a  single  liquid  phase  and  a  single 
crystalline  phase. 

1  VAN'T  HOFF,  Z.  phys.  Chem.,  5,  322  (1890). 


164 


THE   ELEMENTS  OF  METALLOGRAPHY. 


The  simplest  and  most  suggestive  supposition  regarding  the 
crystallization  process  would  be  that  the  crystals  which  are  in 
equilibrium  with  the  melt  possess  not  only  the  same  composition 
among  themselves,  but  also  the  same  composition  as  the  melt. 
There  is,  as  a  matter  of  course,  no  reason  for  supposing  that  a 
separation  of  the  constituents  should  occur  on  crystallization,  if 
they  are  completely  miscible  in  both  the  liquid  and  crystalline 
states.  This  supposition  may  easily  be  tested  according  to 


Time 

FIG.  54. 

p.  32.  We  need  only  take  cooling  curves  of  mixtures  of  various 
concentrations  between  A  and  B.  If  crystallization  occurs  in 
the  manner  suggested  above  (such  that  the  separating  crystals 
are  of  the  same  composition  as  the  remaining  mother  liquor),  we 
have  a  condition  of  complete  heterogeneous  equilibrium  during 
the  whole  process.  The  amount  of  crystalline  material  increases 
and  the  amount  of  melt  decreases,  but  neither  of  the  phases 
changes  its  composition.  Crystallization  must  proceed  at  con- 


TWO  COMPONENT  SYSTEMS.  165 

stant  temperature,  just  as  would  the  case  for  a  pure  substance, 
and  the  cooling  curves  must  show  constant  temperature  halts. 

Experience  teaches  us,  however,  that  our  supposition  is  not 
justified  by  the  facts  in  hand.  In  by  far  the  greater  number  of 
cases,  the  cooling  curves  show  no  halts,  even  in  cases  of  com- 
plete miscibility  in  the  crystalline  condition,  but,  rather,  so-called 
crystallization  intervals.  The  temperature  at  which  the  separa- 
tion of  crystals  begins  is  different  from  the  temperature  at  which 
crystallization  ends.  This  is  made  evident  on  the  cooling 
curves  (Fig.  54),  in  that,  after  the  beginning  of  crystallization  at 
the  point  a,  no  period  of  constant  temperature  ensues,  but  a 
period  of  decreased  rate  of  cooling  instead. 

More  accurate  theoretical  investigation  of  crystallization  pro- 
cesses relating  to  miscibility  in  the  crystalline  condition,  for  which 
we  are  indebted  to  BRUNI'  and  to  RoozEBOOM,2  has  shown  that 
the  above  assumption  fails  of  a  theoretical  basis  as  well.  Before 
proceeding  to  a  discussion  of  these  questions,  we  will  introduce 
a  general  principle  which  was  deduced  by  WILLARD  GiBBS3  from 
theoretical  considerations,  and  which,  among  other  things,  fur- 
nishes information  as  to  when  a  melt  solidifies  without  change 
in  composition  in  a  two  component  system  especially  character- 
ized by  complete  miscibility  in  the  liquid  and  solid  states. 

GIBBS'  PRINCIPLE. 

The  portion  of  this  principle  which  is  of  particular  interest  at 
present  reads:  //,  in  a  two  component  system  consisting  of  two 
phases  in  equilibrium  under  constant  pressure,  the  composition  of 
both  phases  is  the  same,  then  the  temperature,  in  general,  possesses  a 
minimum  or  maximum  value. 

We  will  proceed  to  construe  this  principle  rather  more  definitely 
with  respect  to  its  bearing  upon  solidification  processes  in  a  two 
component  system4: 

In  a  two  component  system  consisting  of  a  single  liquid  and  a 
single  crystalline  phase,  the  composition  of  both  phases  is  the  same 

1  BRUNI,  Rend.  Acad.  Lincei,  1898,  II,  138,  347  (Sept.  4  and  Dec.  18). 

2  ROOZEBOOM,  Acad.  Wiss.  Amsterdam,  Sept.  24,  1898;   Z.  phys.  Chem., 
30,  385  (1899). 

3  GIBBS,  Thermodynamische  Studien  (Ostwald's  translation),  Leipzig,  1892, 
p.  118;  Trans.  Conn.  Acad.,  Hi,  1875-8. 

4  RUER,  Z.  phys.  Chem.,  59,  1  (1907). 


166 


THE  ELEMENTS   OF  METALLOGRAPHY. 


at  those  concentrations  and  at  only  those  concentrations  where  the 
fusion  curve  of  the  concentration-temperature  diagram  (pressure- 
constant)  possesses  a  horizontal  tangent,  viz.,  a  tangent  parallel  to 
the  concentration  axis. 

Thus,  we  are  now  dealing  with  conclusions  which  are  to  be 
drawn  from  the  geometrical  form  of  the  fusion  curve.  The  fol- 
lowing three  cases  represent,  in  broad  generality,  the  possibilities 
of  occurrence  of  curves  with  horizontal  tangent: 

(1)  The  curve  possesses  a  more  or  less  flat  summit,  as  shown  in 
Fig.  55a.     We  have  already  become  familiar  with  this  case,  as 
that  of  a  maximum.     The  tangent  is  indicated  by  a  dotted  line. 

(2)  Analogous  to  the  first  type,  but  represented  by  a  minimum, 
instead  of  a  maximum.     (Shown  in  Fig.  55b.) 

(3)  The  curve  possesses  a  horizontal  inflexional  tangent,  as  in 
Fig.  55c.    Such  a  curve  is  convex  above  and  concave  below.    The 


FIG.  55a. 


FIG.  55b. 


FIG.  55c. 


FIG.  55d. 


point  of  change  in  direction  a  separates  these  two  portions  of  the 
curve.  We  may  regard  this  curve  as  derived  from  the  curve 
shown  in  Fig.  55d,  which  possesses  both  a  maximum  a  and  a 
minimum  6.  On  bringing  the  points  a  and  b  closer  together 
until  they  coincide,  we  obtain  Fig.  55c.  Thus,  a  point  of  change 
in  direction  a,  when  it  constitutes  a  point  on  a  horizontal  tangent 
to  the  curve,  is  also  called  a  maximum-minimum. 

We  will  first  apply  Gibbs'  principle  to  several  previously  dis- 
cussed cases.  It  is  clear  that  the  assertion  made  on  p.  78  that 
never  a  sharp  point,  but  invariably  a  maximum,  is  present  on  the 
fusion  curve  at  the  concentration  of  a  compound  which  melts 
without  decomposition  constitutes  a  special  case  under  this  gen- 
eral principle.  For,  when  two  branches  of  a  curve  meet  in  a 
sharp  point  directed  upwards,  the  tangent  at  this  point  is  not 
horizontal  (rather,  indeterminate).  Again,  we  must  grant,  on  the 
basis  of  our  principle,  that,  e.g.,  in  the  fusion  diagram  of  the  gold- 


TWO  COMPONENT  SYSTEMS.  167 

antimony  alloys  according  to  Vogel  (see  p.  130,  Fig.  37),  the 
curve  branch  BC  runs  horizontally  into  the  point  C.  At  this 
latter  point,  corresponding  to  the  concentration  of  the  pure  com- 
pound, solidification  without  change  in  composition  takes  place, 
and,  hence,  the  branch  of  the  fusion  curve  corresponding  to  this 
crystalline  variety  must  possess  a  horizontal  tangent  at  this 
point.  Since  the  form  of  the  fusion  curve  is,  as  we  are  well 
aware,  very  difficult  to  determine  with  great  accuracy  (see  p.  86), 
it  will  of  course  be  impossible  to  draw  an  accurate  conclusion, 
on  this  basis,  relative  to  the  composition  of  the  compound. 

Our  principle  holds  only  for  a  two  component  system  com- 
posed of  two  phases.  The  melt  must  therefore  solidify  to  a  crys- 
talline variety  of  uniform  composition.  Thus,  we  are  not  able  to 
apply  it  when  the  melt  crystallizes  eutectically,  i.e.,  yields  two 
crystalline  varieties  on  solidification.  The  fusion  curve  possesses 
no  horizontal  tangent  at  the  eutectic  point,  but  a  sharp  point 
directed  downwards,  as  is  well  known. 

Since,  as  we  have  seen,  only  a  single  liquid  and  a  single  crys- 
talline phase  can  occur  if  miscibility  is  complete  in  the  liquid  and 
crystalline  phases,  Gibbs'  principle  must  apply  to  the  crystalliza- 
tion processes  in  all  such  cases.  It  teaches  us  at  once  that,  in 
general,  the  composition  of  the  crystals  will  differ  from  that  of 
the  melt;  that  agreement  in  composition  will  result  only  at  con- 
centrations where  the  fusion  curve  possesses  a  horizontal  tan- 
gent. By  systematic  consideration  of  the  existing  possibilities, 
we  shall  be  able  to  separate  the  cases  wherein  such  concentra- 
tions are  found  in  the  system  from  the  simplest  cases,  wherein  no 
such  concentrations  occur,  and  to  begin  with  a  discussion  of  the 
latter. 

A.  Throughout  all  Concentrations  the  Separated  Crystals  Differ  in 
Composition  from  the  Melt  with  which  they  are  in  Equilib- 
rium. Type  /,  according  to  Roozeboom. 

The  melting  points  of  the  two  metals  A  and  B  are  denoted  in 
the  usual  manner  by  A  and  B.  The  metal  B  melts  at  the  higher 
temperature.  On  determining  the  temperatures  at  which  crystal- 
lization begins  in  the  various  concentrations  (the  points  a  on  the 
cooling  curves  (Fig.  54),  entering  these  temperatures  (points)  in 
a  co-ordinate  system  and  joining  them,  according  to  previous 


168  THE  ELEMENTS   OF   METALLOGRAPHY. 

practice,  we  obtain  the  curve  which  has  been  consistently  called 
the  fusion  curve.  The  fusion  curve  of  course  ends  at  the  melt- 
ing points  of  the  pure  substances  A  and  B.  Concerning  its 
course,  we  may  say,  first  of  all,  that  it  cannot  exhibit  any 
abrupt  change  in  direction.  Breaks,  angles  and  sharp  points 
appear  on  fusion  curves  (and  on  equilibrium  curves  in  general) 
only  where  two  branches  of  the  curve,  each  relating  to  different 
equilibrium  conditions,  intersect.  Such  discontinuity  on  the 
equilibrium  curve  corresponds  to  discontinuous  change  in  the 
system,  e.g.,  consisting  in  the  appearance  of  a  new  crystalline 
variety.  In  such  cases,  we  have  recognized  the  necessity  of  a 
sudden  change  in  the  direction  of  the  fusion  curve,  owing  to  the 
possibility  of  realizing  certain  conditions  which  are  outside  of  the 
stability  jurisdiction  of  the  curve.  But  when  complete  miscibil- 
ity  in  both  the  liquid  and  crystalline  phases  is  prescribed,  the 
composition,  and,  therefore,  the  properties  of  the  crystalline 
variety  which  is  found  in  equilibrium  with  the  melt,  must  vary 
continuously  with  the  composition  of  the  alloy.  Hence,  the 
curve  which  represents  this  equilibrium  must  consist  of  a  single 
branch.  Furthermore,  we  are  able,  in  terms  of  Gibbs'  principle, 
to  say,  relative  to  the  form  of  the  fusion  curve,  that  it  must  con- 
tinually sink  to  lower  temperatures  from  B  toward  A,  as  the  A 
concentration  increases.  For,  pursuant  to  our  original  assump- 
tion that  the  separated  crystals  shall  be  different  in  composition 
from  the  mother  liquor  throughout  all  concentrations,  maxima, 
minima  and  horizontal  inflexional  tangents  may  not  appear  on 
the  curve.  (Since,  according  to  the  above,  the  melting  point  of 
the  lowest  melting  component  A  must  be  raised  by  addition  of 
B,  we  see  that  the  law  of  lowering  of  the  melting  point,  given  on 
p.  38,  which  rests  on  the  assumption  of  non-miscibility  in  the 
crystalline  condition,  actually  fails  of  application  when  this 
special  assumption  is  not  realized.) 

We  are  also  in  a  position  to  make  an  assertion  concerning  the 
composition  of  the  crystals  which  are  in  equilibrium  with  the 
melt  of  certain  definite  concentration.  Use  has  already  been 
made  (p.  39)  of  the  self-evident  proposition  that,  as  long  as 
crystallization  does  not  occur  at  constant  temperature,  the  freez- 
ing point  of  a  mixture  falls  as  freezing  progresses.  Now,  since 
the  fusion  curve  constantly  falls  to  lower  temperatures  as  the  A- 


TWO  COMPONENT  SYSTEMS. 


169 


content  of  the  mixture  increases  (the  freezing  point  of  a  mixture 
lies  deeper  in  proportion  as  the  yl-content  becomes  greater),  the 
above  proposition  means,  in  the  present  case,  that  the  melt  must 
become  richer  in  the  lowest  melting  component  (A)  as  freezing 
progresses.  This  can  obtain  only  in  the  event  that  the  separating 
crystals  contain  more  B  than  the  melt  with  which  they  are  in 
equilibrium. 

We  will  now  take  up  the  further  task  of  determining  not  only 
the  initial  temperatures  of  crystallization,  but  also  the  compo- 
sitions of  the  first  crystals  to  separate  in  successive  concentra- 


Fielc 


Field 
of  Crystals 


10      20      30      40       50      60 
Weight  per  cent  B 

FIG.  56. 


70      80      90     100 


tions  — every  10  per  cent.  If  we  permit  only  a  very  small  amount 
of  the  melt  to  crystallize,  the  composition  of  the  remaining 
mother  liquor  will  agree  within  the  experimental  error  limit  with 
that  of  the  original  melt.  Thus,  only  the  crystals  need  be  ana- 
lyzed. Let  the  results  be  entered  in  a  co-ordinate  system,  and 
the  separate  points  be  joined  to  form  continuous  curves  (Fig.  56). 
Two  curves  are  obtained.  On  the  first,  or  Z-curve  (liquidus),  we 
have  the  temperatures  at  which  melts  of  the  respective  concen- 


170  THE  ELEMENTS  OF  METALLOGRAPHY. 

trations  show  the  first  evidence  of  crystallization.  This  is,  then, 
the  ordinary  fusion  curve.  On  the  second,  or  s-curve  (solidus), 
we  have  the  concentrations  of  the  crystals  which  correspond  to 
each  respective  Z-point.  Both  curves  coincide  at  their  highest 
and  lowest  points  (viz.,  at  the  concentrations  0  and  100).  In  all 
other  concentrations,  the  crystals  are  invariably  richer  in  B  than 
the  melt  from  which  they  have  separated. 

When  complete  miscibility  in  the  crystalline  condition  is  in 
evidence,  the  same  relations  (pp.  165-7)  hold  for  the  s-curve  as 
for  the  Z-curve.1 

The  two  curves  divide  the  Concentration-Temperature  Diagram 
into  three  fields.  Above  the  fusion  curve  All .  .  B,  all  of  the 
material  is  in  the  liquid  condition:  this  is  the  liquid  field.  Below 
the  s-curve,  all  of  the  material  is  in  the  crystalline  condition: 
this  is  the  solid  (crystalline)  field.  Within  the  space  surrounded 
by  both  curves,  crystalline  and  liquid  material  are  associated  in 
equilibrium,  and,  moreover,  the  points  of  intersection  I  and  s  of 
each  horizontal  with  the  two  curves  give  the  respective  compo- 
sitions of  the  melt  and  crystals  which  are  in  equilibrium  at  the 
temperature  of  the  respective  horizontal.  We  are  also  in  posses- 
sion of  information  concerning  the  relative  amounts  of  melt  and 
crystals  of  which  an  alloy  of  given  composition  at  given  tempera- 
ture is  composed  (assuming  equilibrium).  If  both  concentra- 
tion and  temperature  correspond  to  a  point  of  the  Z-curve,  the 
whole  alloy  is  in  the  liquid  condition,  or  the  relative  amount  of 
melt  is  1.  If,  on  the  other  hand,  they  both  correspond  to  a 
point  of  the  s-curve,  the  whole  alloy  is  crystallized.  For  any 
point,  the  relation: 

(Amount  Melt)  .  xl    =  (Amount  Crystals)  .  xs, 
(Amount  Melt)          xs 


or 


(Amount  Crystals)      xl 
holds. 

If  we  assume,  according  to  Roozeboom  (I.e.)  that  equilibrium 
constantly  obtains  during  the  crystallization,   the  diagram  fur- 

1  For  limited  miscibility  in  the  crystalline  condition,  the  s-curve  is  mad 
up  of  separate,  unconnected  branches.     For  complete  immiscibility  in  the 
crystalline  condition,  it  would  be  made  up  of  as  many  verticals,  all  situated 
at  the  concentrations  of  pure  substances  and  compounds,  as  there  were  crys- 
talline varieties  of  different  composition  present. 


TWO  COMPONENT  SYSTEMS.  171 

nishes  us  with  information  on  all  questions  concerning  the  course 
of  the  crystallization.  Suppose  we  consider  the  process  of  crys- 
tallization of  any  chosen  melt,  of  concentration  50  per  cent,  for 
example,  under  this  assumption.  On  cooling,  the  first  separation 
of  crystals  occurs  at  the  temperature  lb.  These  crystals  possess 
the  composition  s5.  Owing  to  separation  of  Pi-rich  crystals,  the 
melt  gradually  becomes  poorer  in  B;  at  the  end  of  a  finite  time  its 
concentration  may  have  become  45  per  cent  B.  The  crystalliza- 
tion temperature  will  then  have  fallen  to  Z4i,  and  the  separating 
crystals  will  then  be  of  the  concentration  s4i  according  to  the 
evidence  of  the  diagram.  But  the  crystals  which  have  separated 
thus  far  and  which  are  richer  in  B  than  s4i  are  not  in  equilibrium 
with  a  melt  of  this  concentration.  We  will  now  assume  that 
cooling  proceeds  slowly  enough  to  allow  the  separated  crystals  the 
necessary  time  for  reaching  equilibrium  with  the  melt  by  diffusion. 
On  this  basis,  we  must  credit  the  components  of  the  crystals 
with  a  very  considerable  capacity  for  diffusion,  which  assumption 
is  indeed  justified  to  a  certain  extent  by  practical  experience  (see 
p.  143).  It  is  true  that  extremely  slow  cooling  is  essential  to  the 
fulfillment  of  this  requirement.  Assuming  that  such  is  effected, 
the  separated  crystals  will  all  possess  the  composition  s4i  when 
the  temperature  and  concentration  of  the  melt  are  given  by  the 
point  l+y  We  may  now  apply  the  relation: 

(Amount  Melt)         s4^a, 
(Amount  Crystals)        l^a ' 

whereby  we  conclude  that  the  alloy  consists  of  s4i  crystals  and 
melt  14±,  in  the  respective  proportions  —  (somewhat  less  than) 
1  part :  (somewhat  more  than)  3  parts.  The  concentration  and  tem- 
perature of  the  alloy  are  represented  by  the  point  a.  When,  after 
further  crystallization,  the  concentration  of  the  melt  has  fallen  to 
40  per  cent  B,  by  reason  of  the  continued  separation  of  5-rich 
crystals,  its  temperature  corresponds  to  the  point  14,  and  the  con- 
centration of  the  crystals  which  are  in  equilibrium  with  this  melt 
corresponds  to  the  point  s4.  Crystals  of  the  concentration  s4± 
would,  therefore,  be  no  longer  in  equilibrium  with  the  melt.  But 
such  crystals  are  no  longer  present,  having  found  time,  in  accor- 
dance with  our  assumption,  to  reach  equilibrium  with  the  melt,  in 
that  they  have  become  so  rich  in  Av  owing  to  reaction  with  the 


172  THE  ELEMENTS  OF  METALLOGRAPHY. 

melt  by  the  time  the  crystallization  temperature  has  fallen  to 
/4,  that  their  composition  corresponds  to  the  point  s4.  Since 
we  have  now  reached  the  point  b  in  the  diagram,  the  alloy 
consists  of  some  45  per  cent  crystals  and  55  per  cent  melt.  The 
process  continues  in  the  above  manner.  When  the  temperature 
has  fallen  to  c,  the  alloy  is  composed  of  crystals  s3  (85  per  cent)  and 
melt  /3  (only  15  per  cent).  Finally,  at  the  point  s  the  s-curve  is 
attained,  and  the  whole  alloy  is  now  solidified  to  a  conglomerate  of 
mixed  crystals  which  one  and  all  possess  the  composition  s  —  50  per 
cent  B,  in  the  present  case. 

If  crystallization  has  progressed  in  this  ideal  manner,  the  cool- 
ing curve  (Fig.  54,  I)  must  show  two  breaks.  Crystallization  has 
begun  at  the  point  a,  whereby  the  rate  of  cooling  has  diminished, 
and  has  ended  at  the  point  b,  whereby  the  rate  of  cooling  has 
regained  its  normal  value,  proceeding  to  completion  in  accord- 
ance with  Newton's  Law.  It  is  clear  that  by  taking  cooling  curves 
of  various  concentrations  we  are  in  possession  of  a  means  of  deter- 
mining not  only  the  course  of  the  Z-curve,  but  that  of  the  s-curve 
as  well,  without  the  least  necessity  for  separating  the  initial  crys- 
tals from  the  melt  —  a  process  which  is  always  difficult  and  in 
many  cases  impossible  —  and  analyzing  them.  For,  just  as  the 
point  a  of  the  cooling  curve  gives  us  a  point  on  the  Z-curve  (corre- 
sponding temperature  and  concentration),  the  point  b  gives  us  a 
point  on  the  s-curve.  As  a  matter  of  fact,  this  procedure,  or  one 
resting  upon  the  same  basis,  is  always  used  in  the  study  of  metallic 
alloys.  The  temperature  difference  between  a  and  b  is  called  a 
crystallization  interval. 

Aside  from  the  question  of  supercooling,  the  determination  of 
points  on  the  Z-curve  (given  by  the  a  points  on  the  cooling  curves) 
is  independent  of  our  original  assumption  relative  to  the  course 
of  the  crystallization  (that  it  be  sufficiently  slow)  and  is,  therefore, 
free  from  objection.  This,  however,  is  not  true  relative  to  the 
determination  of  the  s-curve.  The  points  on  the  s-curve  will 
correspond  to  the  b  points  of  the  cooling  curves  only  when  it 
is  certain  that  equilibrium  between  crystals  and  melt  has  actually 
reached  adjustment,  and  consequently  that,  after  all  crystalliza- 
tion has  ceased,  every  part  of  the  crystalline  conglomerate  possesses 
the  same  composition,  which  must  be  that  of  the  original  liquid 
mixture.  It  may  be  urged,  at  the  outset,  that  this  necessary  con- 


TWO  COMPONENT  SYSTEMS.  173 

centration  adjustment  between  crystals  and  melt  is  never  com- 
pletely realized.  Thus,  a  certain  error  will  always  be  associated 
with  data  concerning  the  course  of  the  s-curve. 

In  order  to  become  familiar  with  the  effect  of  incomplete  con- 
centration adjustment  between  crystals  and  melt,  we  will  follow 
the  crystallization  of  an  alloy  of  the  same  concentration  as  before  — 
50  per  cent  B  —  under  the  assumption  that  this  concentration 
adjustment  fails  entirely  of  realization.  Obviously,  the  initial 
temperature  of  crystallization  a  (Fig.  54,  II),  corresponding  to  /5 
(Fig.  56),  will  not  be  influenced  under  this  new  assumption  (in 
line  with  the  previous  statement  that  the  determination  of  the 
£-curve  is  independent  of  any  special  assumption  pertaining  to  the 
course  of  crystallization).  But,  when  a  certain  amount  of  crystal- 
line material  has  separated  without  attendant  concentration 
adjustment  (such  adjustment  requiring  appropriation  of  A  by  the 
crystals  from  the  melt),  the  melt  is  left  A -richer  than  it  would 
be  if  adjustment  had  occurred,  and  the  temperature  at  which  it 
will  begin  to  crystallize  is  lower  (according  to  the  diagram,  Fig.  40) 
than  it  would  be  under  normal  conditions.  The  curve  branch  ab 
must,  therefore,  show  a  more  rapid  temperature  fall  in  Fig.  54,  II 
than  in  Fig.  54,  I  (representing  ideal  conditions).  Moreover,  the 
concentration  of  the  melt  must  pass  through  all  values  from  the 
initial  concentration,  50  per  cent  B,  up  to  0  per  cent  B  (=  pure  A), 
whereby  the  amount  of  melt  is  continually  reduced.  The  last 
quantity  of  melt,  even  though  inappreciably  small,  must  consist 
of  practically  pure  A.  The  crystals  which  have  separated  during 
the  process  must  likewise  exhibit  all  concentrations  from  s5  down 
to  pure  A,  and  must  also  fall  off  consistently  in  amount  as  the  A- 
content  increases.  The  heat  quantity  which  is  liberated  during 
crystallization  thus  becomes  smaller  and  smaller,  until  finally  the 
zero  value  is  reached  at  the  melting  point  of  A.  Thus  we  see  that 
the  cooling  curve,  Fig.  54,  II,  must  agree  with  the  ideal  curve,  Fig. 
54,  I,  as  far  as  the  point  a,  where  crystallization  first  sets  in,  but 
must  show  a  more  rapid  temperature  fall,  directly  this  point  is 
reached,  than  the  latter.  The  end  point  of  crystallization  b  will 
coincide  with  the  melting  point  of  pure  B,  although  the  quantity  of 
heat  liberated  toward  the  end  of  crystallization  will  have  become 
so  trifling,  owing  to  the  small  remaining  quantity  of  melt,  as  to 
escape  observation.  The  curve  reaches  its  last  stage  at  b  without 


174  THE  ELEMENTS  OF  METALLOGRAPHY. 

discontinuity  (no  break),  thereafter  representing  normal  cooling 
of  the  completely  solidified  alloy  according  to  Newton's  Law. 

Such  crystallization  processes  as  are  actually  realized  in  practice 
will  lie  between  the  extreme  cases  represented  in  Figures  54,  I 
and  54,  II.  Concentration  adjustment  between  crystals  and  melt 
will  develop  to  a  certain  extent,  but  never  completely.  Therefore, 
crystallization  will  practically  cease  at  a  temperature  which  is 
lower  than  that  of  the  point  on  the  s-curve  which  corresponds  to 
the  concentration  in  question,  but  higher  than  the  melting  point  of 
the  lowest  melting  component.  In  any  event,  the  cooling  curves 
must  show  more  extended  crystallization  intervals  (owing  to  in- 
complete concentration  adjustment)  than  are  theoretically  given 
by  the  distances  between  the  points  on  the  I-  and  s-curves  for  the 
respective  concentrations.  Practical  determination  of  the  position 
of  the  s-curve  by  means  of  cooling  curves  will  therefore  result  in  a 
consistently  abnormal  (too  low)  placement  of  the  same.  Such  a 
result  will  approach  the  true  equilibrium  condition  (ceteris  paribus) 
in  proportion  as  the  time  allowed  the  crystals  for  reaching  concen- 
tration adjustment  with  the  melt  is  extended,  i.e.,  in  proportion  as 
cooling  is  retarded.  The  point  b  will  become  less  marked  on  the 
cooling  curve  in  proportion  as  concentration  adjustment  becomes 
less  perfect.  Thus,  under  certain  conditions,  it  will  escape  obser- 
vation. As  a  matter  of  fact,  in  by  far  the  greater  number  of 
cases  wherein  mixed  crystals  are  encountered,  the  point  b  on  the 
cooling  curve  is  only  faintly  perceptible.  This  renders  the  deter- 
mination of  the  s-curve  still  more  uncertain. 

The  form  of  the  £-curve  and  of  the  s-curve  may  be  very  different 
for  different  pairs  of  components.  Figures  57,  58  and  59  repre- 
sent fusion  diagrams,  according  to  RuER,1  of  alloys  of  palladium 
with  the  metals,  copper,  silver  and  gold,  which  constitute  a  natural 
group  of  the  periodic  system. 

According  to  the  evidence  of  these  diagrams,  palladium  forms 
an  unbroken  series  of  mixed  crystals  with  each  of  the  three  metals. 

The  experimentally  determined  points  of  the  Z-curves  are  made 
apparent  by  crosses,  and  the  curve  itself  is  drawn  with  a  heavy 
line.  The  course  of  the  s-curves,  as  derived  from  the  cooling  curves 
by  determination  of  crystallization  intervals,  is  likewise  entered 
in  the  diagrams,  although  these  curves  are  drawn  in  dotted  lines  on 

1  RUER,  Z.  anorg.  Chem.,  51,  223,  315,  391  (1906). 


TWO  COMPONENT  SYSTEMS. 


175 


account  of  the  uncertainty  which  attaches  itself  to  the  method  of 
their  determination.  The  form  of  the  fusion  curve  is  very  different 
in  the  three  diagrams.  We  see  in  the  Palladium-Copper  System 
(Fig.  57)  a  very  gradual  initial  rise  in  the  fusion  curve  (from 
copper  to  palladium),  followed  by  a  very  rapid  rise;  hence,  convex 


1600C 


1500°- 


1400°- 


1300° 


1200 


1100- 


ioooc 


1600° 


1500° 


1400° 


1100* 


0  20  40 

Weight  per  cent  Palladium 


60 


80 


100 


1000° 


FIG.  57.     Fusion  Diagram  of  Palladium-Copper  Alloys. 


curvature  with  respect  to  the  concentration  axis.  In  the  Palla- 
dium-Gold System  (Fig.  59),  just  the  opposite  is  noted:  at  first  a 
rapid  rise  in  the  fusion  curve,  and  finally  a  gradual  rise  from  gold 
to  palladium,  whereby  the  curve  is  concave  with  respect  to  the  con- 
centration axis.  The  fusion  curve  of  the  Palladium-Silver  System 
(Fig.  58)  occupies  an  approximately  mean  position  between  these 
two  extreme  cases.  It  shows  some  curvature,  to  be  sure  (concave 
to  the  concentration  axis),  and  yet  its  form  more  nearly  approaches 
that  of  a  straight  line.  The  following  summary  may  serve  for 


176  THE  ELEMENTS  OF  METALLOGRAPHY. 

1600° , 1 • 1 H 1 1 • 1 • 11600" 


1500° 


1400° 


1300° 


1*00' 


1100C 


1000' 


900° 


10 


)     4(5      (&     <& 


1500° 


1400° 


1300° 


1200° 


1100° 


1000° 


90  100 


900° 


Weight  per  cent  Palladium 
FIG.  58.    Fusion  Diagram  of  Palladium- Silver  Alloys. 

comparison  of  the  relations  thus  characterised  by  the  form  of 
fusion  curve: 

The  melting  point  of  palladium  is  lowered: 


94C 
26C 


by  addition  of 


10  per  cent  Cu, 
10  per  cent  Ag, 
10  per  cent  Au. 


The  addition  of  10  per  cent  palladium  raises  the  melting  point  of 

Cu 7°, 

Ag 98.5°, 

Au....207°. 


TWO  COMPONENT  SYSTEMS. 


177 


It  is  observed  that  the  crystallization  intervals  (given  by  the 
distances  between  the  /-  and  s-curves)  are  uniformly  largest  in  the 
Palladium-Silver  series,  and  smallest  in  the  Palladium-Gold  series. 
They,  of  course,  become  smaller  as  the  pure  metals  are  approached, 
at  which  points  they  reach  the  zero  value.  In  the  Palladium- 
Gold  series  it  is,  moreover,  apparent  that  the  intervals  on  the  gold- 
rich  side  are  larger  than  those  on  the  palladium-rich  side. 


1600C 


1500C 


1400° 


1300° 


1200° L  " 


1100C 


1600° 


1500a 


1400° 


1300C 


1200C 


1100C 


1000C 


10 


20      30     40      50     60     70     80 
Weight  per  cent  Palladium 


90    100 


1000° 


FIG.  59.    Fusion  Diagram  of  Palladium-Gold  Alloys. 

If  crystallization  had  progressed  in  an  ideal  manner,  whereby 
all  the  resulting  crystals  would  have  attained  the  original  composi- 
tion of  the  mixture,  the  structure  of  the  reguli  would  necessarily 
have  been  homogeneous,  as  is  true  in  case  of  pure  substances  (cf. 
Fig.  12a  and  12f).  In  actual  practice,  homogeneous  structure  may 
be  expected  in  those  alloys  alone  which  have  crystallized  within  a 
very  small  interval  of  temperature  (small  crystallization  interval), 
i.e.,  in  which  the  separating  crystals  come  very  close  in  composition 


178  THE   ELEMENTS  OF  METALLOGRAPHY. 

to  the  melt  with  which  they  are  in  equilibrium.  Such  an  interval 
is  to  be  noted  on  the  palladium  side  of  the  Palladium-Gold  System 
: — from  approximately  50  per  cent  palladium  to  100  per  cent 
palladium.  A  section  of  the  60  per  cent  Pd  +  40  per  cent  Au 
alloy,  etched  with  dilute  aqua  regia,  is  shown,  magnified  70  times 
in  Fig.  60.  The  individual  crystalline  polygons  are  very  uniformly 
etched  from  the  center  of  the  section  to  the  sides,  showing  highly 
homogeneous  composition.  The  circumstance  that  a  few  of  the 


FIG.  60.     40%  Au+60%  Pd.     Etched  with  dilute  aqua  regia. 
Magnified  70  times. 

polygons  have  offered  considerable  resistance  to  the  action  of  the 
etching  liquid,  and  have  thus  remained  brilliant,  while  others 
have  been  considerably  attacked  by  the  etching  liquid,  and  thus 
appear  darker  in  the  photograph,  is  directly  traceable  to  the  fact 
that  the  surface  plane  of  the  section  cuts  the  different  crystals  in 
different  directions  (relative  to  the  crystalline  axes).  Phenomena 
of  this  sort  are  associated  with  the  pure  metals  as  well;  particularly 
with  pure  palladium,  as  is  evident  on  consideration  of  Fig.  61, 
representing  a  section  of  this  metal,  etched  with  concentrated  nitric 
acid  and  magnified  70  times.  Here  we  have  polygons  which  have 
remained  brilliant  as  before,  and  are  very  readily  distinguishable 
from  the  darker,  etched  surroundings. 


TWO  COMPONENT  SYSTEMS. 


179 


FIG.  61.     Pure  Palladium.     Magnified  70  times. 


FIG.  62.    30%  Cu+70%  Pd.     Etched  with  dilute  nitric  acid  and  then 
re-polished.      Magnified  70  times. 

If  the  crystallization  interval  is  large,  i.e.,  if  the  crystals  which 
first  separate  differ  considerably  in  composition  from  the  melt,  the 
appearance  of  the  section  will  be  less  uniform.  This  is  well  illus- 
trated by  Fig.  62,  which  represents  a  section  composed  of  30  per 
cent  Cu  +  70  per  cent  Pd,  etched  with  dilute  nitric  acid,  and 


180  THE  ELEMENTS  OF  METALLOGRAPHY. 

then  lightly  re-polished.  According  to  the  diagram,  Fig.  57,  the 
crystals  separating  first  are  richest  in  palladium,  since  palladium  is 
the  higher  melting  component  of  the  system.  These  crystals  have 
served  as  nuclei  for  subsequent  crystallization,  and  are,  accord- 
ingly, enveloped  by  the  material  which  separates — and  becomes 
progressively  richer  in  copper  —  later.  Now,  copper  is  more 
readily  attacked  by  nitric  acid  than  is  palladium,  whence  we 
observe  that  the  polygons  of  this  section  appear  lighter  in  the 


FIG.  63.     70%  Iron +30%  Manganese.     Magnified  40  times. 

interior,  i.e.,  are  less  attacked  here  than  at  the  sides.  Micro- 
scopical examination  of  the  section  in  this  case  shows  conclusively 
that  complete  concentration  adjustment  has  not  taken  place. 

Inhomogeneity  of  the  section  may  be  even  more  marked. 
Fig.  63  shows  a  section  consisting  of  70  per  cent  Fe  +  30  per 
cent  Mn,  magnified  40  times  ;  Fig.  64,  another  section  in  this  series, 
containing  50  per  cent  Fe  +  50  per  cent  Mn,  magnified  100  times. 
The  photographs  are  from  LEVIN  and  TAMMANN'S*  work  on  this 
series.  Two  structure  elements  are  plainly  in  evidence,  namely, 
primarily  separated  crystals,,  which  have  remained  brilliant 
throughout  the  etching  process,  and  a  surrounding  mass,  which 
is  etched  to  a  darker  color.  (A  saturated  solution  of  picric  acid, 
or  an  alcoholic  solution  of  hydrochloric  acid,  served  as  etching 
agent.) 

1  LEVIN  and  TAMMANN,  Z.  anorg.  Chem.,  47,  136  (1905). 


TWO  COMPONENT   SYSTEMS. 


181 


.  On  studying  these  figures,  one  will  scarcely  be  inclined  to 
admit  that  the  results  of  thermal  analysis  in  this  case  (1.  c.), 
indicating  complete  miscibility  in  both  liquid  and  crystalline 
states,  are  correct.  Indeed,  a  plausible  explanation  for  the 


FIG.  64.     50%  Iron +  50%  Manganese  (rapidly  cooled).    Magnified  100  times. 


FIG.  65.     50%  Iron 4-50%  Manganese  (slowly  cooled).     Magnified  100  times. 

appearance  of  these  two  structure  elements  can  hardly  be 
advanced.  Even  if  it  be  assumed  that  the  tendency  toward 
nucleii  formation  is  so  marked  that  envelopment  of  the  crystals 
which  first  separate  by  those  which  follow,  after  the  manner  of 


182  THE  ELEMENTS  OF  METALLOGRAPHY. 

layers,  occurs  to  a  very  limited  extent  only,  it  is,  nevertheless, 
difficult  to  see  how  such  sharply  defined  structure  elements  can 
result.  That  complete  miscibility  in  the  crystalline  condition  -is 
actually  to  be  conceded,  is  apparent  from  Fig.  65,  which  like- 
wise represents  a  section  consisting  of  50  per  cent  Fe  +  50  per 
cent  Mn  (same  concentration  as  that  shown  in  Fig.  64;  also 
magnified  100  times.  But,  while  crystallization  in  the  first  case 
progressed  rapidly,  occupying  some  30  seconds  from  beginning  to 
end,  cooling  was  conducted  so  slowly  in  the  latter  case  that 
approximately  an  hour  elapsed  between  the  initial  and  final 
crystallization.  We  see  that  this  very  slow  cooling  has  resulted 
in  an  almost  completely  homogeneous  structure.  The  section 
shows  large  crystals  separated  from  one  another  by  fine  lines. 
Etching  was  very  uniform  over  the  whole  surface  of  the  crystals. 
(The  black,  drawn-out  oval  spots  correspond  to  air  holes.) 

For  the  purpose  of  rendering  the  alloy  homogeneous,  we  may, 
instead  of  retarding  crystallization,  frequently  obtain  good 
results  by  maintaining  the  crystallized  conglomerate  for  some 
time  at  a  temperature  as  close  as  possible  to  that  of  the  point  on 
the  s-curve  which  corresponds  to  the  concentration  of  the  alloy, 
or,  perhaps,  a  few  degrees  above  this.  The  crystals  may  then  (at 
a  temperature  close  to  their  melting  point)  be  expected  to  reach 
a  certain  concentration  adjustment,  owing  to  diffusion,  particu- 
larly when  such  diffusion  is  facilitated  by  the  presence  of  an 
amount  (even  though  it  be  small)  of  melt.  Nevertheless,  more 
positive  success  is  assured  by  resorting  to  slow  crystallization 
from  the  melt. 

B.  At  Given  Concentrations  the  Separated  Crystals  Possess  the 
Same  Composition  as  the  Melt  with  which  they  are  in  Equi- 
librium. 

According  to  page  166,  the  fusion  curve  must  possess  either  a 
maximum  or  a  minimum  or  a  horizontal  inflexional  tangent  in  such 
cases.  By  combination  of  these  three  simple  cases,  more  com- 
plicated types  are  attained.  No  abrupt  changes  in  direction 
(breaks,  angles  and  peaks)  on  the  /-  and  s-curves  are  possible 
(see  p.  168). 

1.  THE  FUSION  CURVE  POSSESSES  A  SINGLE  MAXIMUM.  TYPE 
II,  ACCORDING  TO  RoozEBOOM.  —  In  this  case,  the  melting  point 


TWO  COMPONENT  SYSTEMS. 


183 


of  the  highest  melting  component  B  must  be  raised  at  the  start 
by  addition  of  A,  as  well  as  the  melting  point  of  the  lowest  melt- 
ing component  A,  by  addition  of  B.  The  Z-curve  is  of  the  gen- 
eral form  shown  in  Fig.  66,  ACB  (drawn  in  full).  The  maximum 
is  at  C.  For  the  purpose  of  acquiring  a  preliminary  conception 
relative  to  the  position  of  the  s-curve,  we  will  again  make  use  of 
the  principle  that,  in  case  a  mixture  fails  to  freeze  at  constant 
temperature,  its  freezing  point  is  lowered  as  material  freezes  out. 
Thus,  according  to  the  /-curve  of  Fig.  66,  if  we  allow  a  melt 


Weight  per  cent  B 
FIG.  66. 


100 


of  some  concentration  between  B  and  C  to  crystallize,  its  melting 
point  can  be  lowered  only  in  that  the  melt  becomes  5-richer  as 
freezing  progresses.  The  separated  crystals  must,  then,  contain 
more  A  than  the  melt  with  which  they  are  in  equilibrium,  i.e., 
the  s-curve  must  run  to  the  left  of  the  Z-curve  in  this  concentra- 
tion area.  From  analogous  considerations,  it  follows  that,  in  the 
concentration  area  between  A  and  C,  the  separated  crystals  must 
contain  more  B  than  the  melt  with  which  they  are  in  equilibrium, 
a  demand  which  is  met  in  the  figure  by  placement  of  the  s-curve 


184  THE  ELEMENTS  OF  METALLOGRAPHY. 

to  the  right  of  the  Z-curve.  The  following  considerations  relating 
to  the  maximum  C  may  be  offered.  On  approaching  this  point 
from  the  A-rich  side  of  the  fusion  curve,  the  separated  crystals 
are  B-richer  than  the  melt,  but,  on  approaching  from  the  B-rich 
side,  the  separated  crystals  are  A-richer  than  the  melt.  Since 
the  presence  of  complete  isomorphism  requires  that  the  compo- 
sition of  the  crystals,  which  are  in  equilibrium  with  a  melt, 
change  continuously  with  continuous  change  in  composition  of 
the  melt,  it  follows  that  at  the  maximum  C  these  crystals  can 
neither  be  richer  in  A  nor  in  B  than  the  melt;  they  must  possess 
the  same  composition  as  the  melt.  Thus,  the  I-  and  s-curves  will 
coincide  at  the  point  C.  There  results,  then,  a  condition  of  com- 
plete equilibrium  at  the  maximum  C:  the  melt  solidifies  after  the 
manner  of  a  pure  substance.  In  this  particular  case,  we  were 
able  to  reach  the  above  conclusion  without  taking  Gibbs'  Prin- 
ciple into  consideration.  The  same  result  follows  on  the  basis 
that,  the  s-curve  (along  which  the  alloy  is  completely  solidified) 
can  never  lie  above  the  Z-curve  (along  which  the  alloy  is  com- 
pletely melted),  and  that  to  every  point  of  the  Z-curve  there  cor- 
responds a  point  of  the  s-curve  for  the  same  temperature. 

Cooling  curves  of  alloys  of  concentrations  between  A  and  C  show 
intervals,  the  magnitudes  of  which  are  given  by  the  respective 
distances  Is  (Fig.  66),  when  crystallization  occurs  in  the  ideal 
manner.  An  analogous  statement  applies  to  alloys  of  concen- 
trations between  C  and  B.  The  cooling  curve  of  an  alloy  which 
corresponds  in  composition  to  the  maximum  C  of  the  fusion  curve 
shows  no  interval,  but,  rather,  a  halting  point,  as  does  a  pure 
substance.  The  structure  of  the  alloys  must  be  completely 
homogeneous  in  all  concentrations. 

If  concentration  adjustment  between  crystals  and  melt  is  im- 
perfectly attained  in  concentrations  between  A  and  C,  the  central 
portions  of  the  crystals  will  be  B-richer  than  the  outside  por- 
tions; in  concentrations  between  B  and  C  the  central  portions 
will  be  A-richer  than  the  outside  portions.  The  structure  of 
an  alloy  of  concentration  C  will  invariably  be  completely  homo- 
geneous. 

No  example  of  this  case  (a  simple  maximum  on  the  fusion  curve 
for  miscibility  in  both  liquid  and  crystalline  states)  is  known  as 


TWO  COMPONENT  SYSTEMS. 


185 


far   as   metallic   alloys   are   concerned.     According  to   ADRIANI,* 
d-  and  /-carvoxim  show  these  relations. 

2.  THE  FUSION  CURVE  POSSESSES  A  SINGLE  MINIMUM.  TYPE 
III,  ACCORDING  TO  RoozEBOOM.  — In  this  case,  the  Z-curve  appears 
as  shown  in  Fig.  67,  ACB  (drawn  in  full).  We  note  in  particular 
that  the  melting  point  of  A  is  lowered  by  addition  of  B,  as  well 


Weight  per  cent  B 
FIG.  67. 


100 


as  the  melting  point  of  B  by  addition  of  A.  The  minimum  is 
situated  at  C.  In  a  manner  analogous  to  that  given  under  Case  1, 
we  decide  that  the  first  crystals  which  separate  in  concentrations 
between  A  and  C  are  A  -richer  than  the  melt;  that  the  first  which 
separate  in  concentrations  between  B  and  C  are  B-richer  than  the 
melt;  and  that,  at  the  point  C,  crystals  and  melt  possess  the  same 
composition.  These  requirements  are  met  in  the  construction  of 
the  diagram  (s-curve  dotted;  /-curve  drawn  in  full). 

The  cooling  curves  of  all  melts  of  concentrations  between  A  and 
C  and  B  and  C  show  crystallization  intervals.  At  the  minimum  C, 
the  alloy  crystallizes  at  constant  temperature,  as  does  a  pure  sub- 

1  ADRIANI,  Z.  phys.  Chem.,  33,  453  (1900). 


186 


THE  ELEMENTS  OF  METALLOGRAPHY. 


stance:  the  cooling  curve  of  this  alloy  shows  a  halting  point. 
For  incomplete  concentration  adjustment  between  crystals  and 
melt  in  concentrations  between  A  and  C,  the  central  portions  of  the 
crystals  are  A -richer  than  the  outside  portions;  while,  in  concen- 
trations between  B  and  C,  the  central  portions  of  the  crystals  are 
5-richer  than  the  outside  portions.  At  the  minimum  C,  the  alloy 
must  be  homogeneous  under  all  conditions. 


Weight  per  cent  B 
FIG.  68. 


100 


Two  metal  pairs,  each  giving  a  fusion  curve  with  simple  minimum, 
have  recently  been  discovered,  namely,  Mn-Cu1  and  Mn-Ni.1,  2 

3.  THE  FUSION  CURVE  POSSESSES  A  SINGLE  HORIZONTAL  IN- 
FLEXIONAL TANGENT.  —  This  case  is  represented  by  Fig.  68.  The 
Z-curve  is  drawn  in  full;  the  s-curve  dotted.  The  course  of  the 
fusion  curve  is  here  quite  similar  to  that  under  Type  I,  according 
to  Roozeboom  (Fig.  56).  The  melting  point  of  B  is  also  lowered  by 
addition  of  A,  and  the  melting  point  of  A  raised  by  addition  of  B. 
The  horizontal  direction  of  the  fusion  curve  at  the  point  of  inflection 

1  ZEMCZUZNYJ,  URASOW  and  RYKOWSKOW,  J.  Russ.  phys.  Chem.  Soc.  7, 
Sept.  20  (1906). 

3  DURDIN.    The  Goettingen  Laboratory  (Tammann). 


TWO  COMPONENT  SYSTEMS. 


187 


C  is  easily  overlooked  in  the  experimental  determination  of  the 
curve.  At  C,  the  melt  solidifies  like  a  pure  substance  (see  p.  165). 
The  cooling  curve  corresponding  to  this  concentration,  therefore, 
shows  a  halting  point,  as  do  the  curves  for  the  pure  substance  A 
and  B,  while  the  cooling  curves  corresponding  to  all  other  concen- 
trations show  crystallization  intervals.  Conversely,  this  con- 
dition, which  will  not  in  general  be  overlooked  on  working  out  the 


Weight  per  cent  B 
FIG.  69. 


100 


fusion  diagram,  demands  a  horizontal  tangent  at  C.  Two  systems 
of  element  pairs  are  known  which,  in  all  probability,  belong  to  this 
type.  These  are  Br-I  and  Mg-Cd.  Discussion  of  these  systems 
is  reserved  for  subsequent  pages.  This  type  is  not  cited  by 
Roozeboom.  On  account  of  the  general  resemblance  of  this  type 
of  fusion  curve  to  Type  I,  we  will  denote  it  as  Type  la. 

4.  MORE  COMPLICATED  FORMS  OF  THE  FUSION  CURVE.  — In  the 
cases  previously  treated,  either  the  melting  point  of  the  lowest  melt- 
ing component  A  is  raised  by  the  first  additions  of  B,  and  that  of 
the  highest  melting  component  B  lowered  by  the  first  additions  of 
A  (Types  I,  la),  or  both  melting  points  are  raised  (Type  II)  or 


188 


THE  ELEMENTS  OF  METALLOGRAPHY. 


lowered  (Type  III)  by  first  additions  of  the  other  (respective)  com- 
ponent. We  may  imagine  a  further  possibility,  namely,  that  the 
melting  point  of  the  lowest  melting  component  A  be  lowered  by  the 
first  additions  of  B,  and  that  of  the  highest  melting  component  B 
raised  by  the  first  additions  of  A.  The  fusion  curve  would  then 
show  a  maximum  as  well  as  a  minimum  (Fig.  69).  The  possibility 
of  such  a  type,  first  advanced  by  NERNST1  relative  to  vapor  pres- 
sure curves,  must  not  be  summarily  rejected  in  the  present  con- 
nection (fusion  curves)  as  long  as  no  definite  assumptions  bearing 


D 


Weight  per  cent  B 
FIG.  70. 


100 


upon  the  molecular  condition  of  the  participating  substances  are 
made.  The  fusion  curve  given  in  Fig.  70  also  shows  a  maximum 
and  a  minimum.  Type  la  may  be  regarded  as  a  limiting  case 
under  this  type.  Finally,  two  maxima  and  one  minimum,  two 
minima  and  one  maximum,  etc.,  might  appear  as  further  compli- 
cations. No  examples  of  these  cases  are  known. 

1  NERNST,  Theoretische  Chemie,  4th  ed.,  p.  113. 


TWO  COMPONENT  SYSTEMS. 


189 


C.   Horizontal  Course  of  the  Fusion  Curve  through  a  Finite 
Concentration  Interval. 

If  the  fusion  curve  runs  horizontally  through  a  finite  concen- 
tration interval,  alloys  of  all  concentrations  which  fall  within  this 
interval  must,  according  to  pp.  165-6,  solidify  after  the  manner 
of  pure  substances.  Such  an  interval  might  reach  as  well  through- 
out the  whole  diagram  as  through  a  portion  of  it.  The  former 
condition  is  shown  in  Fig.  71.  All  mixtures,  as  well  as  the 


A 


I  and  s  Curve 


Weight  per  cent  B 
FIG.  71. 


100 


components  themselves,  solidify  at  the  same  temperature,  after 
the  manner  of  pure  substances.  The  I-  and  s-curves  coincide 
completely.  The  only  known  example  of  this  case  is  the  system 
d-  and  Z-  camphoroxime.1  Owing  to  the  necessary  theoretical 
condition  that  the  melting  points  of  the  two  components  be 
identical,  we  may  well  consider  this  case  restricted  to  optically 
someric  substances;  however,  it  does  not  constitute  a  necessary 
eventuality  even  here.  In  the  case  of  metals,  it  is  excluded  for 
the  above  reason. 


1  ADRIANI,  Z.  phys.  Chem.,  33,  453  (1900). 


190  THE  ELEMENTS  OF  METALLOGRAPHY. 

From  theoretical  considerations,  occurrence  of  the  second  pos- 
sibility, viz.,  a  partly  horizontal  fusion  curve,  appears  improb- 
able. On  the  other  hand,  an  experimental  realization  of  this 
case  —  within  an  error  limit,  on  temperature  observations,  of 
±5  degrees  —  seems  to  have  been  secured  by  GUERTLER  and 
TAMMANN1  in  their  investigation  of  the  system  Co-Fe.  The 
melting  points  of  the  cobalt  steels  between  the  concentration 
limits  100  to  5  per  cent  Co  lie  at  the  melting  temperature 
of  cobalt. 


D.    Polymorphous  Transformations. 

The  thoroughly  different  character  of  the  fusion  diagrams  which 
we  have  lately  described  from  that  of  the  diagrams  previously 
considered  is  due  solely  to  the  circumstance  that,  in  all  the  later 
diagrams,  complete  miscibility  of  the  two  components  in  both 
phase's  constituted  an  essential  condition,  while,  in  the  earlier 
diagrams,  miscibility  in  one  of  the  phases  was  excluded.  We  may, 
therefore,  apply  the  general  deductions  given  on  these  last  pages 
to  all  equilibria  which  refer  to  complete  miscibility  of  the  two  com- 
ponents in  both  of  the  participating  phases.  Let  us  now  assume 
that  each  of  the  substances  is  capable  of  existence  in  two  modi- 
fications: the  a  modifications,  Aa  and  Ba,  stable  at  lower  tem- 
peratures, and  the  ft  modifications,  A$  and  Bp,  stable  at  higher 
temperatures.  Let  the  transitions  be  reversible,  and,  moreover, 
let  the  two  a  modifications,  as  well  as  the  two  ft  modifications,  be 
miscible  in  all  proportions  with  one  another.  Then,  in  completely 
describing  the  transition  phenomena  which  will  result  under  the 
above  assumption,  we  have  only  to  use  Figs.  56,  66,  67  and  68  - 
denoting  the  /-curve,  which  referred  to  liquid  phase  (stable  at 
higher  temperatures),  as  /?-curve,  i.e.,  the  curve  referring  to  the 
crystalline  variety  stable  at  higher  temperatures,  and,  analo- 
gously, the  s-curve  as  a-curve.  Thus,  we  shall  require  to  differen- 
tiate between  the  same  types  of  transformation  curves  as  of  fusion 
curves.  The  a  crystals  which  separate  on  cooling  from  the  ft  crys- 
tals will,  then,  in  general,  differ  from  the  latter  in  composition,  and 
transformation  will  accordingly  take  place  throughout  an  interval. 
If  transformation  occurs  in  an  ideal  manner  (according  to  the 

1  GUERTLER  and  TAMMANN,  Z.  anorg.  Chem.,  45,  205  (1905). 


TWO  COMPONENT   SYSTEMS. 


191 


description  on  p.  171),  the  a  crystals  present  after  complete  trans- 
formation will  all  possess  the  same  composition,  and  this  is  given 


Weight  per  cent  B 
FIG.  72. 


100 


Weight  per  cent  B 
FIG.  73. 


100 


by  the  concentration  of  the  trans- 
forming /?  crystals.  Transformation 
will  occur  at  constant  temperature 
only  in  those  concentrations  which 
correspond  to  pure  substances,  or 
to  certain  characteristic  points  on 
the  diagram. 

Fig.  72 represents  the  combination 
of  a  fusion  diagram  in  which  neither 
maximum  nor  minimum  occurs 
with  a  transformation  diagram  of 
which  the  same  is  true.  Fig.  73 
represents  the  combination  of  a 
fusion  diagram  like  the  above  with 
a  transformation  diagram  in  which 
a  maximum  occurs.  Obviously,  the 
whole  category  of  combination 

among  the  various  equilibrium    types    may    be    made.     When 
only  one  of  the  components,  B,  for  example,  possesses   a  trans- 


Weightper  cent  B 
FIG.  74. 


100 


192  THE  ELEMENTS  OF  METALLOGRAPHY. 

ition  point,  the  condition  of  affairs  shown  in  Fig.  74  will 
result,  according  to  RoozEBOOM.1  The  ft-  and  a-curves  pro- 
ceed from  the  transition  point  of  the  pure  substance  to  lower 
temperatures  and  decreasing  B  concentrations,  without  ever 
reaching  the  concentration,  100  per  cent  A.  The  5-content  of 
mixed  crystals  which  are  A  -richer  than  corresponds  to  the  concen- 
tration D  is  not  great  enough  to  cause  transformation  to  take 
place.  The  system  Cu-Ni2  may  be  mentioned  as  an  example  of 
this  case.  Nickel  changes  to  a  magnetic  modification  at  a  low 
temperature.  However,  reguli  containing  less  than  40  per  cent 
nickel  show  no  action  on  the  compass  needle. 

E.    The  Components   Unite  to  Form  a  Chemical  Compound. 

The  earlier  view  that  a  compound  may  not  form  mixed  crystals 
with  its  components  may  be  regarded  as  effectually  disproven  by 
the  investigations  of  HOLLMAN.S  It  is  nevertheless  true  that 
indisputable  proof  of  the  existence  of  a  compound  between  two 
isomorphous  substances  will  be  obtainable  only  in  rare  cases. 
We  have  no  right  to  assume  such  proof  to  be  at  hand,  as  we  have 
seen  above,  when  a  mixture  of  a  given  concentration  solidifies 
after  the  manner  of  a  pure  substance.  Since  the  law  of  freezing 
point  lowering  does  not  hold  here,  the  presence  of  a  maximum  or 
of  a  minimum  does  not  prove  the  existence  of  a  compound.  On 
the  other  hand,  it  cannot  be  gainsaid  that  the  presence  of  a  maxi- 
mum, etc.,  may  be  due  to  the  existence  of  a  compound.  Proof 
that  the  components  unite  chemically  in  such  cases  will,  then,  be 
forthcoming  only  when  criteria  of  other  nature  (polymorphous 
transformations,  for  example  —  see  below)  are  brought  into  play. 

It  is,  indeed,  true  that  a  method  adapted  in  principle  to  the 
solution  of  this  problem  may  be  proposed.  This  is  completely 
analogous  to  the  method  by  means  of  which  ROSCOE  demonstrated 
that  constant  boiling  mixtures  of  water  and  formic  acid,  water 
and  hydrochloric  acid,  etc.,  are  not  chemical  compounds.  The 
composition  of  a  chemical  compound  must  be  independent  of  the 
method  of  preparation  of  the  compound,  and  Roscoe  was  able  to 

1  ROOZEBOOM,  Z.  phys.  Chem.,  30,  413  (1899). 

2  GUERTLER  and  TAMMANN,  Z.  anorg.  Chem.,  52,  27  (1906). 

3  HOLLMAN,  Z.  phys.  Chem.,  37,  193  (1901). 


,.    TWO  COMPONENT  SYSTEMS.  193 

show  that  this  condition  fails  to  obtain  in  the  above  cases;  that  the 
composition  of  these  constant  boiling  mixtures  is  dependent 
on  the  pressure  under  which  distillation  is  effected.  In  precisely 
the  same  manner,  it  may  be  determined  that  the  maximum,  etc., 
of  the  fusion  curve  is  due  to  chemical  combination  when,  and  only 
when,  its  concentration  is  independent  of  the  pressure  under  which 
fusion  occurs.  Unfortunately,  considerable  difficulty  is  associated 
with  the  practical  application  of  this  method  in  the  present 
connection,  since  the  effect  of  external  pressure  on  the  processes 
which  take  place  in  the  crystalline  and  liquid  phases  is  very 
slight  in  comparison  to  its  effect  on  those  which  relate  to  the 
gas  phase. 

Perhaps  we  are  most  inclined  to  decide  in  favor  of,  or  against, 
the  acceptation  of  a  compound,  according  as  the  maximum,  etc., 
does,  or  does  not,  correspond  to  a  simple  formula. 

Of  the  two  systems,  I-Br  and  Mg-Cd,  each  of  which  shows  a 
point  of  inflection  with  horizontal  tangent  upon  its  fusion  curve, 
in  the  first,  the  concentration  of  this  point  very  probably  corre- 
sponds, and  in  the  second  most  certainly  corresponds,  to  a  com- 
pound. It  is  to  be  expected  that  this  will  always  be  the  case,  for, 
from  theoretical  considerations,1  the,  to  a  certain  extent,  chance 
occurrence  of  such  a  point  is  very  improbable;  in  any  event,  less 
probable  than  that  of  a  maximum  or  minimum,  which  is  itself 
represented  by  very  few  known  examples. 

1.  THE  SYSTEM:  BROMINE-IODINE.  — Fig.  75  gives  the  fusion 
diagram  of  the  system  Br-I,  according  to  MEERUM  TERWOGT.2 
The  concentration  axis  is  graduated  in  atomic  per  cent  iodine. 
We  see  that  the  Z-curve  apparently  sinks  continuously  from  the 
melting  point  of  pure  iodine  (+  110.6  degrees)  to  that  of  pure 
bromine  ( —  7.3  degrees).  It  is  met  by  the  s-curve  close  to  the  con- 
centration, 50  per  cent  iodine,  for  concentrations  between  50  and  53 
atomic  per  cent  I  solidify  completely  within  a  temperature  interval 
of  1  degree,  i.e.,  nearly  after  the  manner  of  pure  substances.  The 
close  agreement  of  this  particular  concentration  with  that  corre- 
sponding to  the  formula  IBr  renders  the  existence  of  a  compound 
of  such  formula  extremely  probable.  If  the  compound  possesses  a 
sharp  melting  point,  then  the  tangent  to  the  Z-curve  at  this  con- 

1  RUER,  Z.  phys.  Chem.,  59,  6  (1907). 

2  MEERUM  TERWOGT,  Z.  anorg.  Chem.,  47,  203  (1905). 


194 


THE  ELEMENTS  OF  METALLOGRAPHY. 


centration  will,  according  to  p.  166,  be  horizontal,  and,  for  com- 
plete isomorphism,  coincidence  of  the  /-  and  s-curves  must  cor- 
respond with  that  shown  in  the  vicinity  of  the  point  C  in  Fig.  68 
(p.  186).  The  s-curve  in  the  Br-I  System  actually  possesses  a 
point  of  inflection  at  about  50  per  cent  I,  and  the  inherent  uncer- 
tainty of  the  determination  at  once  permits  of  the  assumption  that 


100 


FIG.  75. 


0.4          0.6 

Concentration 


Fusion  Diagram  of  the  System  Bromine-Iodine  according  to 
Meerum  Terwogt. 


the  tangent  is,  in  reality,  horizontal  at  this  point.  Admitting  that 
an  error  of  from  1  to  2  degrees  may  apply  to  the  temperature  deter- 
mination of  the  Z-curve,  the  existence  of  a  point  of  inflection  with 
horizontal  tangent  within  the  concentration  limits,  50  to  53  per 
cent  I  may  be  assumed. 


TWO  COMPONENT  SYSTEMS. 


195 


550° 


450 


350° 


250 


150 


100 


Mg 


\              ••) 
\ 
\ 

\ 

^ 

S 

^ 

2 

r^^ 

D 

X 

^ 

"x 

V 

N 

F 

*1 

a> 

1 

\\ 

\ 

<H 

2. 

35      5. 

14      8, 

50     12 
Ator 

62    17 

lie  per  t 

81  24 
ent  Cad 

58    33 
mium 

53    46 

43    66 

10      I 

10         20         30         40         50         60         70 

Weight  per  cent  Cadmium 


80 


90 


Cd 


100 


FIG.  76.    Fusion  Diagram  of  Magnesium-Cadmium  Alloys 
according  to  Grube. 

2.  MAGNESIUM-CADMIUM  ALLOYS.  —  Fig.  76  gives  the  fusion 
diagram  for  the  Mg-Cd  System,  as  constructed  by  GRUBE l  on 
the  basis  of  experimental  cooling  curves.  The  /-curve,  ABC,  is 
drawn  in  full  and  the  s-curve,  AD  EEC,  dotted.  Both  curves  coin- 
cide at  the  point  B  where  the  crystallization  interval  becomes  zero, 

1  GRUBE,  Z.  anorg.  Chem.,  49,  72  (1906). 


196  THE  ELEMENTS  OF  METALLOGRAPHY. 

i.e.,  an  alloy  of  this  composition  solidifies  after  the  manner  of  a  pure 
substance.  The  concentration  of  the  point  B  corresponds  to  the 
formula  MgCd,  requiring  82.19  per  cent  Cd;  the  experimentally 
determined  course  of  the  /-  and  s-curves  also  permits  of  the  assump- 
tion in  this  case  that  a  horizontal  tangent  occurs  at  B.  Con- 
ceding the  possibility  of  a  few  degrees'  error  in  the  temperature 
determination,  there  can  be  no  doubt  here  that  the  concentra- 
tion B  corresponds  to  a  definite  compound ;  for  the  alloy  in  ques- 
tion sustains  polymorphous  transformation  on  further  cooling, 
a  condition  foreign  to  either  of  the  pure  components,  magne- 
sium and  cadmium.  When  the  diagram  is  divided  at  the  con- 
centration B,  two  single  (and  complete)  diagrams  are  obtained, 
each  of  which  corresponds  to  the  type  shown  in  Fig.  52.  The 
highest  temperature  at  which  transformation  occurs  is  given  by 
the  point  F  of  concentration  B.  Moreover,  transformation  (at 
F)  is  completed  at  constant  temperature,  as  the  theory  requires  for 
a  pure  substance,  while,  at  neighboring  concentrations,  an  interval 
of  transformation  obtains.  Since,  as  previously  noted,  the  pure 
components  are  incapable  of  transformation,  these  curves  (FG, 
etc.)  end  before  the  concentrations  0  (pure  Mg)  and  100  (pure 
Cd)  are  reached. 

§  4.  THE  LIQUID  STATE  is  CHARACTERIZED  BY  COMPLETE  MISCI- 
BILITY;  THE  CRYSTALLINE  STATE  BY  INCOMPLETE  MISCI- 
BILITY. 

The  condition  of  limited  miscibility,  as  it  applies  to  two  liquids, 
has  been  exhaustively  discussed  on  p.  149  et  seq.  When  we 
limit  ourselves  to  consideration  of  the-  crystalline  state,  the  essen- 
tial features  of  the  diagram  given  in  Fig.  48,  which  represents  the 
corresponding  relations  for  the  liquid  state,  may  be  brought  into 
play.  For  every  temperature,  there  exist  concentrations,  a  and 
b,  which  are  in  equilibrium  with  one  another,  and  which  we 
designate  as  saturated  mixed  crystals.  Using  the  previously 
chosen  method  of  characterization,  we  designate  the  mixed 
crystals  of  A,  saturated  with  B  at  the  corresponding  tempera- 
ture tlt  as  a±  mixed  crystals,  and,  likewise,  the  mixed  crystals  of 
B,  saturated  with  A  at  the  temperature  tlt  as  6X  mixed  crystals.  If 
the  concentration  of  an  alloy  corresponds  to  a  point  without  the 


TWO  COMPONENT  SYSTEMS. 


197 


solubility  curve,  only  one  crystalline  variety  is  present;  if  it 
corresponds  to  a  point  within  the  area  surrounded  by  the  solu- 
bility curve,  then  the  crystalline  phase  has  separated  into  two 
crystalline  varieties,  namely,  A  mixed  crystals  and  B  mixed 
crystals,  each  saturated  at  the  corresponding  temperature,  just 
as  a  liquid  phase  separates  into  two  layers  under  similar  con- 
ditions. The  concentrations  of  these  two  varieties  of  saturated 
mixed  crystals  will  be  given  by  the  intersections  of  the  solu- 
bility curve  with  a  horizontal  corresponding  to  this  temperature. 
The  lever  relation  also  supplies  information  concerning  the  relative 
amounts  of  the  two  varieties  in  the  present  case.  The  condition 
represented  in  Fig.  48,  viz.,  that  miscibility  increases  with  the 
temperature,  and  that  the  two  saturation  concentrations  a  and  b 
approach  closer  to  one  another  as  the  temperature  increases,  will 
be  considered  generally  descriptive  of  the  crystalline  state  as  well. 
On  this  point,  we  are  well  in  accord  with  practical  experience. 

In  two  respects,  however,  direct  application  of  the  diagram- 
matic relations  deduced  for  the  liquid  state  to  the  crystalline  state 
requires    amplification    or    modifi- 
cation,  as  the   case    may    be.     In 
the  first  place,   a  difference  is  evi- 
dent, in  that  the  area  of  stability 
for    the    crystalline    state    lies    at 
lower   temperatures   than    for    the 
liquid   state.     Thus,  there  is  little     , 
possibility  of  encountering  an  ex-     j 
ample  of  the  fusion  diagram  shown 
in   Fig.    77.     It    is    assumed    here     j 
that,     after     homogeneous     solidi- 
fication   has    occurred,    separation 
ensues;    represented    in    the    usual 
manner    by    the    m-curve.      That 
we    have   thus   far   failed   to   find 
an  actual  example  of  this  type,  in 
which    the    upper    portion    of    the 
solubility    curve    for    the    crystal- 
line  state   is   realized,    is   presumably  due  to  the  circumstance 
(apart  from  any  consideration  of  the  difficulty  which  is  asso- 
ciated with  determination  of  the  solubility  curve  (see  p.  202)) 


Weight  per  cent  B 
FIG.  77. 


100 


198 


THE  ELEMENTS  OF  METALLOGRAPHY. 


that  this  curve  has  invariably  met  the  s-curve  for  the  equi- 
librium, liquid  crystalline,  at  some  inferior  position,  whereby  this 
upper  portion  has  been  eliminated.  The  same  condition  which 
sets  a  limit  to  the  realization  of  the  solubility  curve  for  liquids 
below  certain  temperatures  (see  p.  154)  hinders  the  realization  of 
this  curve  for  the  crystalline  state  above  certain  temperatures. 
Thus,  the  solubility  curve  for  the  two  crystalline  varieties  reaches 
its  natural  end  at  the  temperature  tlt  at  which  fusion  begins,  and 


Weight  per  cent  B 
FIG.  78. 


100 


Weight  per  cent  B 
FIG.  79. 


100 


therefore  consists  of  two  separate  branches.  Now,  in  general,  the 
compositions  of  melt  and  crystals,  in  equilibrium  with  one  another, 
are  different,  as  we  are  well  aware.  Hence  we  grant  that  the 
melt  appearing  at  any  given  temperature  will  be  of  different 
composition  from  the  crystals  with  which  it  is  in  equilibrium, 
and  reserve  the  consideration  of  special  cases  in  which  melt  and 
crystals  possess  the  same  composition  for  subsequent  pages  (see 
pp.  207  and  211).  Two  cases  are,  then,  possible:  The  composition 
c  of  the  melt  lies  either  at  a  concentration  which  is  situated 
between  the  two  saturated  mixed  crystals  at  and  6t  (Fig.  56),  or 
at  a  concentration  which  is  richer  in  one  of  the  two  components 
of  the  system;  in  A,  for  example  (Fig.  79).  In  the  first  case 
(Fig.  78),  reaction  between  both  crystalline  varieties  a^  and  6t 


TWO  COMPONENT  SYSTEMS.  199 

is  necessary  for  production  of  melt,  and  we  write  the  descriptive 
equation: 

Sat.    Mixed    Crystals    al  +  Sat.    Mixed    Crystals    ^ 


On  heating,  this  reaction  proceeds  from  left  to  right.  We  have 
here  complete  equilibrium,  whence  the  temperature  tl  will  remain 
constant  until  one  of  the  phases  becomes  exhausted.  If  the  total 
concentration  of  the  system  corresponds  to  the  point  c,  then  neither 
crystalline  variety  will  be  present  after  completion  of  the  reaction, 
but  all  of  the  material  will  exist  in  the  liquid  condition.  If  the 
total  concentration  lies  between  av  and  c,  however,  crystals  of  the 
concentration  al  will  remain  in  contact  with  melt  after  reaction; 
if  it  lies  between  bl  and  c,  crystals  of  the  concentration  bi  will 
remain.  Thus,  in  the  two  latter  cases,  further  elevation  of  tem- 
perature is  necessary  for  complete  fusion,  and  we  readily  see  that 
the  straight  line  alcbl  must  be  covered  by  two  branches  of  the 
/-curve,  both  of  which  intersect  at  the  point  c,  and  one  of  which 
corresponds  to  equilibrium  between  A  -rich  crystals  and  melt;  the 
other,  to  equilibrium  between  B-rich  crystals  and  melt  (Fig.  78). 

In  the  second  case  (Fig.  79),  when  the  melt  is  ^.-richer  than  either 
of  the  two  crystalline  varieties  at  and  6t  with  which  it  is  in  equi- 
librium, it  is  obviously  impossible  to  obtain  melt  c  from  any 
mixture  of  al  and  6r  This  melt  can  be  formed  only  in  the  following 
manner.  The  A-richer  of  the  two  varieties  of  crystals,  namely,  the 
saturated  at  mixed  crystals,  yield  melt  of  composition  c,  while 
their  excess  of  B  is  not  liquefied,  but  plays  its  constituent  part  in  a 
crystalline  residue  of  B-saturated  A  mixed  crystals,  correspond- 
ing in  composition  to  the  point  bv  as  previously  noted.  At  the 
temperature  tlt  then,  the  saturated  mixed  crystals  al  disappear,  in 
that  they  fall  to  melt  c  and  saturated  mixed  crystals  6t.  The 
equation  of  the  reaction  reads: 

Sat.  Mixed  Crystals  al  +±  Melt  c  +  Sat.  Mixed  Crystals  6t. 

We  have  here,  as  before,  complete  equilibrium,  whence  the 
temperature  tl  will  remain  constant  until  one  of  the  phases  becomes 
exhausted. 

On  continued  heat  addition  at  the  temperature  tv  the  A-rich 
crystals  al  disappear  completely.  After  the  temperature  has  been 
increased  just  beyond  this  point,  B-rich  crystals  only  will  remain 


200  THE  ELEMENTS  OF  METALLOGRAPHY. 

unfused,  some  higher  temperature  being  required  for  their  fusion. 
Thus,  only  a  single  branch  of  the  /-curve  —  corresponding  to  equi- 
librium between  melt  and  jB-rich  crystals  —  can  exist  above  the 
straight  line  caf)v 

On  considering  the  course  of  the  above  reaction  from  right  to 
left  (on  cooling),  we  see  that  all  concentrations  between  6t  and  c 
must  be  concerned  in  the  change.  If  the  mixed  crystals  6t  and 
melt  c  are  present  in  such  proportions  that  their  average  concen- 
tration (the  total  concentration  of  the  system)  corresponds  to  the 
point  al  (saturated  A. -rich  mixed  crystals),  all  of  the  material  will 
have  become  solidified  to  al  mixed  crystals  after  the  reaction  has 
proceeded  to  completion.  If  the  bl  crystals  are  present  in  excess, 
i.e.,  if  the  average  concentration  lies  between  al  and  61?  we  shall  have 
complete  solidification  at  the  temperature  tl}  as  in  the  above  case, 
but  the  conglomerate  will  now  consist  of  at  and  6t  mixed  crystals. 
Finally,  if  melt  c  is  present  in  excess,  i.e.,  if  the  average  concen- 
tration lies  between  al  and  c,  melt  c  will  still  remain  after  com- 
pletion of  the  reaction,  and  its  concentration  cannot  change  until 
the  temperature  falls  again.  As  long  as  the  total  concentration 
of  the  alloy  lies  between  c  and  bv  melt  c  and  mixed  crystals  6t  must 
exist  in  the  presence  of  one  another  when  the  temperature  has 
fallen  to  tr  Not  until  the  point  c  is  reached,  does  the  quantity  of 
these  mixed  crystals  become  zero.  It  follows  from  the  above  dis- 
cussion that: 

(1)  The  branch  of  the  /-curve   corresponding  to  equilibrium 
between  B  crystals  —  stable  at  higher  temperatures  —  and  melt 
must  meet  the  line  a161  at  c,  and  that, 

(2)  A  branch  of  the  /-curve  running  to  lower  temperatures,  and 
corresponding    to   equilibrium    between    A-rich    mixed    crystals, 
stable  at  lower  temperatures,  and  melt,  must  join  the  other  curves 
at  c  (Fig.  79). 

To  summarize,  then,  we  note  that,  for  incomplete  miscibility  in 
the  crystalline  state,  two  different  forms  of  fusion  diagram  may 
develop,  according  to  the  particular  composition  of  the  melt  c. 
Roozeboom  arranges  the  cases  represented  in  Figs.  79  and  78  in 
sequence  with  the  three  cases  of  complete  isomorphism  (according 
to  his  classification),  whereby  they  constitute  Types  IV  and  V, 
respectively.  Both  types  will  be  discussed  at  greater  length 
shortly. 


TWO  COMPONENT  SYSTEMS.  201 

A  second  difference  between  incomplete  miscibility  in  the  liquid 
and  crystalline  states  is  determined  by  the  fact  that,  on  the  part 
of  crystalline  bodies,  there  remains  the  factor  of  specific  crystal- 
line form,  in  addition  to  that  of  composition,  to  be  duly  con- 
sidered. On  general  principles,  we  would  have  here  two  cases  to 
differentiate,  according  to  whether  both  saturated  mixed  crystals 
of  the  components  A  and  B  crystallized  in  the  same  or  in  different 
forms.  We  should,  then,  distinguish  the  first  case,  that  of  "limited 
isomorphism,"  from  the  second,  that  of  "isodimorphism."  Ob- 
viously, a  classification  of  this  sort  does  not  apply  to  liquid  solu- 
tions. However,  we  shall  disregard  any  differences  of  this  sort  in 
the  present  connection,  since  the  fusion  diagrams  for  both  cases 
agree  in  those  particulars  to  which  we  limit  our  observations;  and 
let  it  remain  undecided  whether  the  mixed  crystals  a  and  b  do  or 
do  not  differ  in  form. 

Finally,  we  should  allude  to  the  fact  that  the  recovery  of  equi- 
librium during  temperature  changes  which  are  accompanied  by 
changes  in  composition  of  all  the  crystals,  in  such  alloys  as  possess 
concentrations  within  the  limits  of  the  solubility  curve,  calls  for  a 
very  considerable  power  of  diffusion  on  the  part  of  the  substances 
A  and  B  which  are  dissolved  in  the  crystals. 

A.    Type  IV,  according  to  Roozeboom. 

The  complete  fusion  diagram  representing  this  case,  the  essential 
characteristics  of  which  we  have  already  noted,  is  shown  in 
Fig.  80.  The  Z-curve  ACB  is  susceptible  to  very  close  determina- 
tion, limited  only  by  the  accuracy  of  the  temperature  measure- 
ments; provided,  of  course,  that  supercooling  is  absent.  This 
curve  is,  therefore,  drawn  in  full,  as  is  the  horizontal  CDE,  along 
which  the  previously  considered  reaction: 

Sat.  Mixed  Crystals  E  +  Melt  <=±  Sat.  Mixed  Crystals  D 

takes  place  at  constant  temperature  (ti)  from  left  to  right  on  ab- 
straction of  heat. 

According  to  the  above,  then,  a  change  in  stability  takes  place 
along  this  horizontal.  At  temperatures  above  CDE  (  =  tj,  the 
J3-rich  crystals  are  stable,  while,  at  temperatures  below  CDE,  the 
J.-rich  crystals  are  stable.  Hence,  the  /-curve  ACB  shows  a 


202 


THE  ELEMENTS  OF  METALLOGRAPHY. 


break  at  the  temperature  tlf  falling  more  gradually  from  C  than  it 
rises  from  the  same  point    (see  p.  123). 

The  s-curve,  consisting  of  the  two  separated  portions  BE  and 
DA  which  give  the  compositions  of  crystals  corresponding  to 
different  melts  at  different  temperatures,  is  drawn  in  dotted  lines 
for  the  purpose  of  indicating  that  exact  determination  of  these 


e     \a 


Weight  per  cent  B 
FIG.  80. 


100 


concentrations  is  subject  to  the  same  difficulty  as  was  noted 
under  Type  I  (complete  isomorphism).  This  difficulty  becomes 
manifest  to  a  still  greater  extent  in  the  determination  of  the  two 
branches  of  the  solubility  curve  which  are  capable  of  realization 
up  to  the  temperature  limit  t^  since  the  heat  of  mixture  for  the 
crystalline  phase  is  probably  extremely  slight,  as  is  the  case 
relative  to  the  liquid  phase.  For  this  reason  the  process  of 
separation  is  not  indicated  by  the  cooling  curve.  (A  second 
reason  for  the  circumstance  that  no  actual  observation  of  the 
theoretically  required  break  on  the  cooling  curve  at  the  initial 


TWO  COMPONENT  SYSTEMS.  203 

temperature  of  separation  ever  materializes  could  lie  in  an 
insufficient  rapidity  of  the  process.) 

Suppose  we  consider  the  crystallization  process  in  molten 
alloys  of  various  composition,  under  the  assumption  that  it  is 
ideal,  whereby  cooling  proceeds  so  slowly  that  equilibrium  con- 
tinually obtains. 

Let  an  alloy  numbered  1  have  some  concentration  inter- 
mediate between  E  and  100  per  cent  B  (Fig.  80).  When  the 
temperature  has  fallen  to  the  point  llf  the  /-curve  is  reached  and 
crystallization  begins.  The  composition  of  the  separating  crys- 
tals will  then  be  given  by  the  point  st  of  the  s-curve,  which  cor- 
responds to  the  temperature  of  lr  Since  the  separating  crystals 
are  bound  to  constantly  maintain  a  condition  of  equilibrium 
with  the  melt,  in  the  manner  described  on  p.  171,  this  melt  will 
have  solidified  to  a  conglomerate  of  mixed  crystals,  all  possessing 
the  composition  s'  of  the  original  mixture,  by  the  time  the  tem- 
perature has  fallen  to  s'.  In  consequence,  the  cooling  curve  of 
this  alloy  can  show  but  one  interval,  namely,  one  reaching  from 
lt  to  s'. 

The  structure  of  sections  taken  from  the  solidified  alloy  will, 
nevertheless,  be  completely  homogeneous  only  when  the  vertical 
numbered  1  utterly  fails  to  cut  the  solubility  curve  of  the  two 
crystalline  varieties,  or  fails  to  cut  it  except  at  some  temperature 
below  that  at  which  the  section  is  subjected  to  examination.  Let 
us  make  the  assumption  that  the  structure  of  all  sections  is 
investigated  at  the  temperature  zero  of  our  co-ordinate  system; 
the  same  considered  to  be  room  temperature.  Then  the  inter- 
section q  of  this  vertical  with  the  branch  EG  of  the  solubility 
curve  lies  above  the  temperature  of  examination,  and  we  shall 
observe  a  mixture  of  two  different  crystalline  varieties,  namely, 
A-saturated  B  mixed  crystals  and  B-saturated  A  mixed  crystals, 
into  which  the  originally  homogeneous  crystals  have  subsequently 
separated  (unaccompanied  by  noticeable  heat  effect).  The  con- 
centrations of  these  crystals  correspond  to  the  points  F  and  G, 
while  their  relative  amounts  are  given  by  the  lever  relation. 

Let  an  alloy  numbered  2  have  some  concentration  intermediate 
between  D  and  E.  The  vertical  numbered  2  cuts  the  Z-curve  at 
the  point  12.  Initial  separation  of  crystals  occurs  at  this  tem- 
perature, and  these  crystals  have  the  composition  s2.  When  the 


204  THE  ELEMENTS  OF  METALLOGRAPHY. 

temperature  has  fallen  to  that  of  the  horizontal  CDE,  the  alloy 
consists  of  melt  of  composition  C  and  crystals,  which,  on  account 
of  the  previously  assumed  idealistic  concentration  balance,  are 
uniformly  of  concentration  E.  If  heat  is  further  removed  from 
the  system,  an  increased  lowering  of  temperature  does  not  at  once 
result;  the  first  thing  that  occurs  is  transformation  of  .B-rich 
saturated  mixed  crystals  E  +  melt  into  A  -rich  saturated  mixed 
crystals  D,  after  the  manner  previously  noted.  This  reaction 
persists  until  the  melt  is  entirely  exhausted.  The  alloy  has 
then  become  completely  solidified,  and  consists  of  the  two  crystal- 
line varieties  D  and  E.  At  this  point,  further  abstraction  of  heat 
causes  temperature  fall,  accompanied  by  alteration  in  compo- 
sition of  these  crystals  along  the  curve  branches  DF  and  EG, 
until  the  temperature  of  the  surroundings  is  reached.  In  line 
with  our  general  assumptions,  the  J3-rich  crystals  will  possess  the 
composition  G,  and  the  A-rich  crystals,  the  composition  F. 
Since  this  last  change  along  DF  and  EG  has  proceeded  without 
noticeable  heat  effect,  the  cooling  curve  will  show  no  added 
peculiarity  over  and  above  its  break  at  12  and  its  halting  point  at 
the  temperature  of  the  horizontal  CDE. 

Let  an  alloy  numbered  3  have  some  concentration  intermediate 
between  C  and  D.  Initial  separation  of  crystals  occurs  at  the 
temperature  13.  These  crystals  have  the  composition  s3.  When 
the  temperature  has  fallen  to  that  of  the  horizontal  CDE,  the 
whole  alloy  consists  of  melt  C  and  B-rich  crystals  of  concentra- 
tion E,  as  did  alloy  2  at  this  temperature.  On  further  abstraction 
of  heat,  transformation  of  these  B-rich  crystals  +  melt  into  the 
crystalline  variety  D  occurs.  When  this  reaction  has  proceeded 
to  completion,  no  B-rich  crystals  are  left,  and  the  alloy  consists  of 
^.-rich  crystals  of  composition  D  and  melt  C.  (Only  when  the 
composition  of  the  alloy  corresponds  exactly  to  the  point  D  are 
melt  and  crystalline  variety  E  present  in  such  proportions  that 
both  are  exhausted  when  reaction  has  ceased.)  Further  solidifi- 
cation of  the  melt  C  follows  the  branch  CA  of  the  /-curve,  whereby 
the  composition  of  the  crystals  with  which  it  is  in  equilibrium  is 
given  by  the  branch  DA.  In  accordance  with  our  assumption  of 
complete  concentration  balance  between  crystals  and  melt,  the 
latter  will  have  become  completely  solidified  by  the  time  the 
temperature  s'"  is  reached,  and  will  now  be  replaced  by  a  conglom- 


TWO  COMPONENT  SYSTEMS. 


205 


erate  of  homogeneous  crystals  of  this  composition.  Relative  to 
subsequent  separation  in  the  event  of  intersection  of  vertical 
number  3  with  the  branch  DF  of  the  solubility  curve,  the  remarks 
offered  under  alloy  1  are  pertinent.  In  line  with  the  above 
description,  the  cooling  curve  of  such  an  alloy  (Fig.  81)  shows  a 
break  at  13,  an  interval  between  the  temperature  13  and  that  of 
the  horizontal  CDE,  a  halting  point  at  the  latter  temperature, 
and  finally  another  interval  reaching 
from  this  temperature  to  the  tem- 
perature s'". 

The  last  series  of  cooling  curves, 
those  furnished  by  alloys  inter- 
mediate between  C  and  A  in  con- 
centration, are  similar  to  the  first 
series  (B—E);  they  show  a  single 
interval. 

The  length  of  the  periods  of  con-    | 
stant  temperature  which  correspond    | 
to  reaction  at  the  horizontal  CDE    f 
reaches  its  maximum,  as  is  apparent    ^ 
from   the   equation  of  the   reaction 
given  earlier,   at   the    concentration 
D,  and  decreases  linearly  toward  C 
and  E,  where  the  zero  value  obtains. 
This   is  indicated  in  the   figure  by 
the    thin    line   cde    which  joins   the 
end  points  of  verticals  erected  upon 
the    concentration  axis  as  base,  at 
lengths  proportional  to  these  periods 

in  the  corresponding  concentrations.  Observation  of  these  periods 
thus  constitutes  a  method  of  determining  the  position  of  the 
points  C,  D  and  E. 

The  structure  of  sections  is  homogeneous  between  0  (=  pure  A) 
and  F,  and  again  between  G  and  100  (=  pure  B).  Between  F 
and  G,  two  varieties  of  crystals  appear  in  the  sections;  for  the 
included  range  D-E,  these  consist  of  primarily  separated  satu- 
rated B-rich  mixed  crystals  surrounded  by  saturated  A -rich  mixed 
crystals,  which  have  been  formed  secondarily  by  reaction  at  the 
temperature  of  the  horizontal,  while  for  the  rest  of  these  concen- 


Time 
FIG.  81. 


206 


THE  ELEMENTS  OF  METALLOGRAPHY. 


trations,  namely,  the  ranges  F-D  and  E-G,  the  alloys  consist 
entirely  of  A -rich  or  B-rich  mixed  crystals,  respectively,  just  after 
solidification,  and  become  inhomogeneous  only  after  the  curve 
branches  DF  and  EG  have  been  cut  on  further  cooling.  It  is  clear 
that  abnormalities  due  to  incomplete  concentration  balance  (to  be 


(!>>,  I 


Weight  per  cent  B 
FIG.  80a. 


100 


generally  expected)  will  be  productive  of  results  similar  to  those 
described  under  the  case  of  complete  isomorphism  (see  p.  177). 
Other  abnormalities,  due  to  incomplete  reaction  between  crystal- 
line variety  E  and  melt,  may  obtain  here.  We  have  become 
acquainted  with  the  same  general  condition  in  the  case  of  the  con- 
cealed maximum  (see  p.  134  et  seq.). 

The  system  Hg-Cd1  serves  as  an  example  of  this  type.  Here, 
the  gap  in  miscibility  at  the  temperature  of  complete  equilibrium 
is  comparatively  small.  A  very  considerable  gap  in  miscibility 
was  observed  by  ISAAC  and  TAMMANN,Z  relative  to  the  system 

1  BIJL,  Z.  phys.  Chem.,  41,  641  (1902). 

2  ISAAC  and  TAMMANN,  Z.  anorg.  Chem.,  53,  281  (1907). 


TWO  COMPONENT  SYSTEMS.  207 

Fe-Au.    We  should  note,  along  with  the  above  citation  of  examples, 
that  this  type  is  of  comparatively  infrequent  occurrence. 

The  following  limiting  cases  under  Type  IV  may  be  obtained: 

(1)  We  suppose  here  that  the  concentration  difference  between 
melt  C  and  the  crystalline  variety  D  continues  to  decrease  until  C 
and  D  coincide.     Fig.  80a  represents  the  conditions  corresponding 
to  such  coincidence.     Since  solidification  occurs  after  the  manner  of 
a  pure  substance  at  D,  both  the  /-  and  s-curves  DA  must  enter  D 
horizontally,  i.e.,  they  must  possess  a  horizontal  tangent  in  this 
vicinity   (see  p.    165).     The  systems  Au-Cd,1  Ag-Zn2  and  Cu-Zn 
(brass)3  are,  in  all  probability,  examples  of  this  case. 

(2)  We  grant  that  the  gap  in  miscibility  DE  (Fig.  80)  continu- 
ally becomes  smaller  (i.e.,  that  the  points  D  and  E  continually 
approach  one  another),  until  it    disappears    completely.4     Thus 
we  develop  the  case  of  complete  isomorphism  —  Type  I,  according 
to   Roozeboom   (Fig.   56).     The   break  C  on   the  Z-curve   must 
obviously  disappear  also,  since  only  one  variety  of  mixed  crystals 
can  now  be  existent  at  all   temperatures.     In  consequence,  no 
halting  points  (brought  about  by  disappearance  of  one  crystalline 
variety)  may  appear  on  the  cooling  curves. 

(3)  We  grant  that  all  three  points  C,  D  and  E  coincide.     Then 
Type  la  (Fig.  68),  in  which  the  fusion  curve  possesses  a  point  of 
inflection  with  horizontal  tangent,  results. 

(4)  We  grant  that  the  gap  in  miscibility  for  the  crystalline  state 
continually  becomes  larger  until  the  concentrations  D  and  E  corre- 
spond to  the  pure  substances,  viz.,  lie  at  0  and  100  respectively. 
Then  the  point  C,  which  corresponds  to  the  composition  of  the 
melt,  must  obviously  become  coincident  with  D,  and,  therefore, 
with  A  also,  i.e.,  the  lower  branch  CA  must  disappear.     In  this 
way,  we  are  led  to  the  diagram  shown  in  Fig.  14  (p.  71),  which  type 
was  previously  shown  to  be  a  limiting  case  for  complete  immis- 
cibility  in  the  crystalline  state  —  deduced  by  imagining  one  branch 
of  the  fusion  curve  to  continually  become  shorter  and  finally  dis- 
appear.    In  terms  of  the  above,  we  see  that  this  same  type  appears 
as  limiting  case  for  the  conditions  which  we  have  been  considering 
on  these  latter  pages. 

1  VOGEL,  Z.  anorg.  Chem.,  48,  333,  (1906). 

2  PETRENKO,  Z.  anorg.  Chem.,  48,  347,  (1906). 

3  SHEPHERD,  Journ.  Phys.  Chem.,  8,  421,  (1904). 

4  The  curve  of  separation  is  not  considered  in  this  connection. 


208 


THE  ELEMENTS  OF  METALLOGRAPHY. 


B.    Type  V,  according  to  Roozeboom. 

The  essential  features  of  this  type  have  already  been  anticipated. 
The  complete  melting-point  diagram  is  to  be  found  in  Fig.  82. 
The  Z-curve  ACB,  as  well  as  the  horizontal  DCE,  are  drawn  in 
heavy  lines  because  they  may  be  readily  determined  thermally, 


Weight  per  cent  3 
FIG.  82. 


100 


while  both  portions  of  the  s-curve  AD  and  BE,  as  well  as  both 
portions  of  the  solubility  curve  DF  and  EG,  are  drawn  in  thin  lines 
because  they  are  not  susceptible  to  accurate  determination  ther- 
mally, or,  indeed,  to  any  such  determination  at  all  in  some  instances. 
At  the  horizontal  DCE,  the  following  reaction  takes  place  toward 
the  right  at  the  constant  temperature  ^  when  heat  is  abstracted: 

Melt  C  ±^  Sat.  Mixed  Crystals  D  +  Sat.  Mixed  Crystals  E. 


TWO  COMPONENT  SYSTEMS.  209 

The  duration  of  the  halting  points  which  appear  upon  the  cool- 
ing curves,  owing  to  solidification  during  this  reaction,  has  its 
maximum,  according  to  the  above  equation,  at  the  concentration 
C,  and  decreases  lineally  toward  the  concentrations  D  and  E, 
where  it  becomes  zero.  This  is  indicated  in  the  figure,  according  to 
usual  custom,  by  a  line  DcE,  which  joins  the  end  points  of  verticals 
erected  upon  the  base  (horizontal)  line  DCE  at  lengths  which  are 
proportional  to  the  halting  periods.  The  determination  of  these 
halting  periods  thus  constitutes  a  means  of  locating  the  three  points 
C,  D  and  E. 

A  melt  1,  of  concentration  between  0  (=  pure  A)  and  D,  first 
separates  crystals  of  composition  st  at  the  temperature  l^  Assum- 
ing that  complete  concentration  balance  obtains,  the  alloy  will  have 
completely  solidified  to  a  conglomerate  of  crystals,  all  possessing  the 
same  concentration  as  the  original  mixture,  by  the  time  its  tem- 
perature has  fallen  to  s'.  Whether  a  subsequent  separation  of  these 
homogeneous  crystals  into  two  saturated  mixed  crystals  will  occur 
on  further  cooling  to  the  temperature  of  the  surroundings  (taken  as 
0  degrees  in  our  coordinate  system),  depends  upon  whether  the 
corresponding  vertical  cuts  the  portion  DF  of  the  solubility  curve 
or  not.  Since  a  process  of  this  sort  is  not  accompanied  by  a  very 
considerable  heat  effect,  merely  one  interval,  of  the  magnitude 
li  s',  will  be  observed  upon  the  cooling  curve  in  each  and  every 
case. 

Alloy  2,  of  concentration  between  D  and  C,  first  separates  crys- 
tals of  the  composition  s2  at  the  temperature  12.  When  the  tem- 
perature has  fallen  to  that  of  the  horizontal  DCE,  the  melt  will 
possess  the  concentration  C,  and  the  entire  body  of  crystals,  the 
concentration  D.  Complete  solidification  at  constant  temperature 
will  now  ensue,  whereby  saturated  mixed  crystals  of  the  two 
varieties  D  and  E  are  formed.  The  cooling  curve  consequently 
shows  an  interval  beginning  at  the  temperature  12  and  ending  at  the 
temperature  ^  (that  of  the  horizontal  DCE),  followed  by  a  halting 
point  at  the  latter  temperature.  The  change  in  composition  of 
the  saturated  mixed  crystals  D  and  E  along  the  curves  DF  and 
EG  on  further  decrease  in  temperature  is  not  revealed  by  the 
cooling  curve. 

An  alloy  of  composition  C  solidifies  like  a  pure  substance.  A 
single  halting  point  is  present  upon  the  cooling  curve. 


210  THE  ELEMENTS  OF  METALLOGRAPHY. 

What  was  said  relative  to  alloy  2  applies  to  concentrations 
between  C  and  E,  except  that  we  now  have  crystals  of  the  com- 
position E  in  equilibrium  with  the  (same)  melt  C  when  the 
temperature  has  fallen  to  that  of  the  horizontal  DCE. 

Remarks  relative  to  alloy  1  apply  to  concentrations  between 
E  and  100  (=  pure  B). 

The  structure  of  sections  of  the  different  reguli  (investigated  at 
ordinary  temperature)  between  0  and  F  and  between  G  and  100 
must  be  homogeneous.  Sections  of  concentrations  between  F 
and  G  show  mixed  crystals  of  B  in  A  and  of  A  in  B,  correspond- 
ing to  concentrations  F  and  G  respectively  (i.e.,  saturated  at 
ordinary  temperature),  side  by  side.  Primarily  separated  A-rich 
mixed  crystals  of  concentration  D  at  the  temperature  of  the 
horizontal  DCE,  must  appear  in  concentrations  between  D  and 
C.  These  are  surrounded  by  a  mixture  of  D  and  E  crystals, 
which,  owing  to  its  manner  of  formation,  must  reveal  an  eutectic 
structure.  Since  the  concentration  differences  between  D  and  F 
and  between  E  and  G  are,  in  general,  only  trifling,  changes  which  take 
place  at  temperatures  below  that  of  the  horizontal  DCE  will  cause 
no  marked  changes  in  the  structure  of  the  sections.  In  sections 
of  concentrations  between  C  and  E,  the  primarily  separated  crystals 
will  all  possess  the  composition  E  at  the  temperature  of  the  hori- 
zontal DCE.  The  secondary  mixture  of  D  and  E  crystals  which 
has  been  formed  on  crystallization  of  the  residue  of  melt  at  this 
temperature  is  the  same  as  that  present  in  concentrations  between 
D  and  C.  The  originally  homogeneous  structure  of  alloys  between 
D  and  F  and  E  and  G  becomes  inhomogeneous,  owing  to  subsequent 
separation. 

Incomplete  concentration  balance  between  the  crystals  which 
first  separate  in  concentrations  0  to  F,  or  G  to  100,  and  melt  will 
primarily  result  in  an  inhomogeneous  (for  the  most  part  zonal) 
structure.  Moreover,  in  the  case  of  concentrations  which  are 
A -richer  than  D,  and  5-richer  than  E,  an  appreciable  amount  of 
melt  of  concentration  C  will  finally  be  left,  whereby  the  point  D 
will  be  displaced  toward  the  A  -rich  side,  and  the  point  E  toward 
the  J5-rich  side.  Thus,  determination  of  the  interval  DE  is 
rendered  uncertain.  This  is  the  same  condition  which  effects  an 
extension  of  the  melting  interval,  i.e.,  a  displacement  of  the 
portions  AD  and  BE  of  the  s-curve  toward  lower  temperatures 


TWO   COMPONENT  SYSTEMS. 


211 


(see  p.  174).     For  remarks  concerning  the  reduction  of  this  defect 
by  means  of  slow  cooling,  etc.,  see  p.  182. 

The  following  cases  can  be  realized  as  limiting  cases  of  Type  V: 

(1)  We  assume  here  that  the  concentration  difference  between 

melt  C  and  the  crystalline  variety  D  (Fig.  82)  continually  decreases, 

so  that  C  and  D  finally  coincide.     Fig.  82a  represents  this  case  for 

coincidence  of  the  points  C  and  D  (at  C).     At  the  point  C,  uniform 


Weight  per  cent  B 
FIG.  82a. 


100 


solidification  occurs,  whereby,  according  to  p.  166,  the  CA  portion 
of  both  the  I-  and  s-curves  must  possess  a  horizontal  tangent  at 
C.  It  is  clear  that  there  are  two  different  possible  types  of  curve 
for  the  case  wherein  the  melt  with  which  both  saturated  mixed  crys- 
tals are  in  equilibrium  possesses  the  same  composition  as  one  of  the 
crystalline  varieties  (Figs.  80a  and  82a),  according  to  whether  we 
regard  it  as  the  limiting  case  of  Type  IV  or  of  Type  V.  Obviously, 


212 


THE  ELEMENTS  OF  METALLOGRAPHY. 


it  will  be  found  very  difficult  in  practice  to  determine  whether  D 
and  C  coincide  perfectly  or  not.  Cases  which,  in  any  event,  closely 
approximate  the  conditions  represented  in  Fig.  80a  are  frequently 
observed  (compare,  for  example,  R.  RUER,  Z.  anorg.  Chem.,  52, 
355  (1907)). 

(2)  In  this  case,  we  imagine  the  gap  in  miscibility  DE  (Fig.  82) 
to  become  continuously  smaller,  until  finally  the  two  points  D 


Weight  per  cent  B 
FIG.  82b. 


100 


and  E  and  the  intermediate  point  C  become  coincident.  Thus 
we  obtain  the  case  of  unlimited  miscibility,  wherein  the  melting- 
point  curve  possesses  a  maximum,  shown  in  Fig.  45.  We  may, 
therefore,  obtain  Type  III  as  a  limiting  case  of  Type  V. 

(3)  On  the  other  hand,  we  may  imagine  the  gap  in  miscibility 
to  become  continuously  larger,  i.e.,  the  points  D  and  E  to  con- 


TWO  COMPONENT  SYSTEMS.  213 

stantly  retreat  from  one  another  (Fig.  82b).  In  this  case,  the 
saturated  A  mixed  crystals  become  continuously  5-poorer  and 
the  saturated  B  mixed  crystals  continuously  A -poorer.  If  D  and 
E  finally  meet  the  temperature  axis,  the  substances  A  and  B, 
respectively,  separate  from  all  melts  in  the  pure  condition,  i.e., 
we  have  the  case  first  considered  (p.  56),  and  represented  by 
Fig.  lla  (" Complete  miscibility  in  the  liquid  state,  complete 
immiscibility  in  the  crystalline  state,  no  compounds  and  no 
polymorphous  transformation  ")  as  a  limiting  case  under  Type  V. 
In  fact,  the  specification  of  complete  immiscibility  in  the  crys- 
talline state  when  no  compounds  are  existent  merely  signifies 
that  the  composition  of  the  crystals  which  are  in  equilibrium  with 
melts  of  all  concentrations  must  correspond  to  the  concentrations 
0  or  100,  viz.,  to  pure  A  or  pure  B.  We  should  note,  in  this  con- 
nection, that  it  is  impossible  in  practice  to  determine  with  cer- 
tainty whether  or  not  the  limiting  case  of  complete  immiscibility 
is  at  hand.  We  simply  find  ourselves  in  a  position  to  designate 
an  outside  limit  beyond  which  there  can  be  no  miscibility  in  the 
crystalline  state,  and  this  limit  will  become  more  rigorous  in 
proportion  as  the  adopted  methods  of  investigation  improve  in 
accuracy  (see  p.  69).  Theoretical  considerations  even  demand 
that  a  condition  of  absolute  immiscibility  be  fundamentally 
excluded.  Nevertheless,  experience  has  shown  that  this  con- 
dition may  be  so  closely  approximated  that  we  are  justified  in 
using  the  term  complete  immiscibility  in  a  practical  sense,  and  in 
neglecting  the  extremely  limited  miscibility  which  always  obtains 
in  such  cases,  but  which  is  not  revealed  experimentally.  Part  of 
the  modern  theory  of  solution  is  based  upon  this  disregard  of 
inappreciable  solubilities,  and  the  brilliant  agreement  of  theoretical 
conclusions  with  the  results  of  general  experience  further  supports 
the  rectitude  of  such  idealization.  In  principle,  Fig.  82b  repre- 
sents the  mutual  behavior  of  two  substances  more  correctly  than 
the  limiting  case,  Fig.  lla. 

The  mutual  solubility  of  the  two  substances  (invariably  present, 
according  to  theory)  will  vary  with  the  temperature;  in  general 
becoming  less  as  the  temperature  falls.  This  is  indicated  by  the 
portions  DF  and  EG  (Fig.  82b)  of  the  curves  of  incomplete 
equilibrium,  which  give  the  equilibrium  concentrations  of  both 
crystalline  varieties  in  their  relation  to  the  temperature,  and 


214  THE  ELEMENTS  OF  METALLOGRAPHY. 

which,  in  accordance  with  the  above  statements,  may  practically 
coincide  with  the  temperature  axes. 

The  main  difference  between  the  two  melting-point  diagrams 
given  in  Figs.  82  and  82b,  as  opposed  to  that  given  in  Fig.  11  a, 
may  be  thus  defined:  in  the  first  case,  the  horizontal  DCE  ends 
before  the  concentrations  of  the  pure  substances  are  reached, 
while,  in  the  second  case,  it  reaches  throughout  the  whole  diagram 
(p.  69).  The  horizontal  DCE  is  known  in  all  cases  as  the  eutectic 
horizontal. 

Cooling  curves  of  alloys  whose  concentrations  lie  between  D  and  E 
(Fig.  82)  and  which,  in  consequence,  show  eutectic  halting  points 
are  not  different  in  form  from  those  of  alloys  whose  components 
do  not  appreciably  mix  in  the  crystalline  state.  For  example, 
on  the  cooling  curve  of  alloy  2,  a  period  of  eutectic  crystallization 
follows  the  crystallization  interval  beginning  at  12  and  ending  at 
the  temperature  of  the  eutectic  horizontal.  The  process  of 
crystallization  during  this  interval  is,  indeed,  different  from  the 
analogous  process  pertaining  to  complete  immiscibility  in  the 
crystalline  state.  In  the  first  case,  the  composition  of  the  crystals 
changes  as  they  continue  to  be  formed,  and,  provided  normal 
concentration  balance  is  maintained,  that  of  the  previously 
separated  crystals  also  changes  continuously  as  tne  temperature 
falls,  while,  in  the  second  case,  the  same  crystals  are  deposited 
from  the  beginning  to  the  end  of  the  process.  On  the  cooling 
curve  this  difference  is  not  evident.  A  break  is  observed  on  the 
cooling  curve  of  alloy  2  at  the  initial  temperature  of  crystalliza- 
tion 12,  from  which  point  a  retarded  fall  in  temperature  ensues, 
owing  to  heat  evolution  attending  the  separation  of  crystalline 
material.  At  the  temperature  of  the  eutectic  horizontal,  this 
retarded  temperature  fall  is  succeeded  by  a  period  of  constant 
temperature.  Thus  we  have  just  the  sort  of  curve  which  would 
have  resulted  in  the  entire  absence  of  miscibility  in  the  crystalline 
state.  In  place  of  a  conglomerate  composed  of  the  pure  substances 
A  and  B  (corresponding  to  complete  immiscibility),  the  cold 
alloys  of  concentrations  between  D  and  E  (neglecting  the  possibility 
of  any  subsequent  separation)  consist  of  the  saturated  mixed 
crystals  D  and  E,  of  which  one  variety  occurs  as  primary  crystals 
and  as  a  constituent  of  the  eutectic,  and  the  other  variety  purely 
as  a  constituent  of  the  eutectic. 


TWO  COMPONENT  SYSTEMS.  215 

Very  many  examples  of  this  type  might  be  cited.  It  is  the  most 
frequently  observed  type  of  melting-point  diagram  of  two  com- 
ponents which  mix  completely  in  the  liquid  state  and  form  no 
chemical  compounds  with  one  another.  By  a  strict  interpreta- 
tion, the  system  Antimony-Lead  (p.  72)  would  properly  belong 
here,  since,  according  to  the  above,  we  are  not  justified  in  attribu- 
ting complete  absence  of  mutual  miscibility  to  these  components. 
In  the  systems  Au-Cu1  and  Ag-Cu,2'3  mutual  solubility  of  the 
components  in  the  crystalline  state  is  well  marked.  Still  greater 
miscibility  is  to  be  observed  in  the  system  Au-Ni.4  Considerable 
miscibility  appears  on  the  aluminium  side  in  the  system  Al-Zn5' 6; 
trifling  miscibility  on  the  zinc  side. 

C.    Polymorphous  Transformations. 

If  polymorphous  transformations  occur  after  completion  of  crys- 
tallization, the  mutual  miscibility  of  the  a  crystals,  stable  at  the 
lower  temperature,  may  be  greater  or  lesser  than  that  of  the 
ft  crystals,  first  separating.  In  case  the  /?  crystals  (which  have 
separated  from  the  melt)  are  miscible  in  all  proportions,  while 
the  a  crystals  show  a  gap  in  their  miscibility,  earlier  explanations 
serve  as  well  in  this  connection  by  way  of  presenting  an  adequate 
exposition  of  the  prevailing  conditions.  We  have  here,  as  before, 
equilibrium  between  one  phase  in  which  complete  miscibility 
occurs  and  another  characterized  by  incomplete  miscibility. 
Moreover,  since  the  transition  from  complete  to  incomplete 
miscibility  is  affected  by  lowering  the  temperature,  it  follows  that 
Types  IV  and  V,  with  which- we  have  become  familiar  for  the  case 
of  liquid-crystalline  equilibrium,  when  combined  with  the  types 
which  represent  complete  isomorphism,  must  adequately  describe 
the  mutual  relations  of  the  two  substances  in  question.  Thus, 
Fig.  83  shows  the  melting-point  diagram  of  two  substances  A  and 
B  which  first  solidify  to  a  complete  series  of  /?-mixed  crystals, 
according  to  Roozeboom's  Type  I.  On  further  abstraction  of 

1  ROBERTS  AUSTIN  and  KIRKE  ROSE,  Proc.  Roy.  Soc.,  67,  105  (1900). 

3  HEYCOCK  and  NEVILLE,  Phil.  Trans.,  189a,  25  (1897). 

8  OSMOND,  Bull.  soc.  Encouragement,  5th  series,  2,  837  (1897). 

4  LEVIN,  Z.  anorg.  Chem.,  45,  238  (1905). 

6  HEYCOCK  and  NEVILLE,  Jour.  Chem.  Soc.,  71,  383  (1897). 
•  SHEPHERD,  Jour.  Phys.  Chem.,  9,  504  (1905). 


216 


THE  ELEMENTS  OF  METALLOGRAPHY. 


heat,  transformation  into  crystals  stable  at  lower  temperatures  will 
occur  in  all  concentrations.  These  a  crystals  are  not  capable  of 
as  extended  mutual  solubility  as  the  /?  crystals,  whereby  transfor- 
mation must  follow  either  Type  IV  or  Type  V,  which  latter  con- 
dition is  represented  in  the  figure.  The  case  shown  in  Fig.  84 


Weight  per  cent  B 
FIG.  83. 


100 


in 


is  somewhat  different.  Here,  the  ft  crystals  exhibit  a  gap 
miscibility,  according  to  Type  IV,  while  the  a  crystals  are  com- 
pletely miscible  with  one  another.  This  diagram  cannot  be 
obtained  by  simple  combination  of  the  types  which  have  already 
been  studied,  since  it  includes  limited  miscibility  of  the  modifica- 
tions stable  at  higher  temperatures.  The  fact  that  the  central 
concentrations  are  not  composed  of  crystals  of  a  single  variety 


TWO   COMPONENT   SYSTEMS. 


217 


is  responsible  for  the  association  of  discontinuity  with  the  trans- 
formation of  /?  crystals  into  the  continuous  series  of  a  crystals. 
At  the  temperature  a,  where  the  transformation  curve  cuts  the 
solubility  curve  of  the  /?  crystals,  there  are  present  not  only 


Weight  per  cent  B 
FIG.  84. 


100 


saturated  mixed  crystals  a  of  the  /?  modification,  but  also  the  sat- 
urated mixed  crystals  b,  likewise  of  this  modification,  and  crys- 
tals of  the  a  modification  of  concentration  c  (stable  at  all  lower 
temperatures),  all  in  equilibrium  (compare  the  similar  case  — 
p.  153).  On  abstraction  of  heat,  the  temperature  remains  con- 
stant until  the  reaction: 


a 


b  +  c 


218  THE  ELEMENTS  OF  METALLOGRAPHY. 

has  proceeded  to  completion,  i.e.,  until  the  a  crystals  have  been 
used  up. 

Finally,  if  we  make  the  assumption  that  the  /?  crystals,  as  well 
as  the  a  crystals,  are  incompletely  miscible,  the  relations  become 
very  complicated.  Detailed  information  on  this  point  may  be 
obtained  from  Roozeboom's  paper,  "  Umwandlungspunkte  bei 
Mischkristallen. "  l 

D.    The  Components  Unite  to  Form  a  Chemical  Compound. 

On  combining  two  melting-point  diagrams  of  the  form  shown  in 
Fig.  82,  we  obtain  the  single  diagram  given  in  Fig.  85.  Here,  both 
components  A  and  B  are  partially  miscible  with  the  compound 
C  =  AmBn  in  the  crystalline  state.  Determination  of  the  com- 
position of  the  compound  is  difficult  in  such  cases,  since  the 
eutectic  horizontals  ab  and  cd  do  not  end  at  the  concentration  cor- 
responding to  the  composition  of  the  compound,  but  at  the  con- 
centrations of  the  A -rich  and  B-rich  mixed  crystals,  respectively. 
There  remains  a  single  criterion  by  which  the  composition  must  be 
judged,  namely,  determination  of  the  position  of  the  maximum  C 
on  the  melting-point  curve,  in  connection  with  the  fact  that 
solidification  must  occur  without  change  of  temperature  at  this 
concentration,  i.e.,  the  melting  interval  must  be  zero  at  this  point. 
The  uncertainty  reaches  so  far  in  this  case  that  we  are,  conversely, 
unable  to  draw  a  positive  conclusion  regarding  the  question  of 
chemical  combination  between  two  substances  when  they  show  the 
mutual  relations  given  in  Fig.  85.  For  we  know  that  the  law  of 
depression  of  the  melting  point,  from  which  our  inferences  (see 
p.  76)  are  drawn,  holds  only  when  there  is  no  miscibility  in  the 
crystalline  condition,  viz.,  when  the  composition  of  the  crystalline 
variety  which  separates  from  the  melt  within  certain  concentra- 
tion intervals  is  practically  independent  of  the  composition  of  the 
melt.  If  this  condition  is  not  realized,  as  is  true  in  the  present  case 
relative  to  those  concentrations  which  lie  between  b  and  c,  our 
deductions  in  the  above  connection  fail  to  be  conclusive.  Thus, 
we  would  not  be  justified  in  concluding  from  the  presence  of  a 
maximum  C  that  a  chemical  compound  of  this  composition  is 
existent,  as  long  as  we  are  not  certain  that  the  position  of  C  is  inde- 

1  ROOZEBOOM,  Z.  phys.  Chem.,  30,  413  (1899). 


TWO  COMPONENT  SYSTEMS.  219 

pendent  of  the  pressure  on  the  system,  and  experimental  evidence 
relating  to  the  latter  point  is  not  readily  obtainable. 

On  the  other  hand,  it  is  to  be  emphasized  that  the  mutual  rela- 
tions of  the  two  substances  A  and  B  are  described  in  the  most 
natural  and  unconstrained  manner  under  the  assumption  that  a 
compound  AmBn  exists.  Otherwise,  the  existence  of  two  gaps  in 
miscibility  would  have  to  be  conceded.  In  the  case  of  liquids,  no 
such  condition  occurs  —  more  than  one  gap  in  miscibility  is  never 
observed,  i.e.,  at  a  given  temperature  only  two  liquids  of  different 
composition  (namely  a  saturated  solution  of  B  in  A  and  a  satu- 
rated solution  of  A  in  B)  are  capable  of  existing  in  equilibrium  with 
one  another.  In  the  crystalline  state,  the  possibility  of  existence 
of  several  gaps  in  miscibility  cannot  be  contradicted  a  priori,  since 
we  must  here  regard  the  question  of  crystalline  form  in  addition 
to  that  of  solubility  as  a  second  factor  of  importance.  Such  a 
double  gap  in  miscibility  might  find  an  explanation  in  limited 
isomorphism  of  the  two  components,  associated  with  isodimorphism 
(see  p.  201). *  An  example  of  the  case  just  discussed  is  furnished  by 
the  system  Mg-Ag,  according  to  the  investigation  of  ZEMCZUZNYJ2. 
Here  a  compound  (of  the  formula  MgAg)  undoubtedly  corre- 
sponds to  the  maximum  C  (Fig.  85).  In  addition,  the  existence  of 
a  compound  of  the  formula  Mg3Ag,  which  does  not  melt  unchanged, 
was  proven.  Further  illustration  of  this  case  is  offered  by  the 
systems  Au-Zn3  and  Ni-Si.4 

Fig.  86  may  be  regarded  as  a  combination  of  Types  IV  and  V, 
and  is,  therefore,  traceable  to  a  double  gap  in  miscibility.  An  inter- 
pretation recognizing  the  existence  of  a  concealed  maximum  in 
this  type  will  appear  simpler  and  more  natural.  The  case  is  then 
analogous  to  that  shown  in  Fig.  33  (p.  115),  except  that  limited 
miscibility  in  the  crystalline  state  characterizes  the  mutual  rela- 
tions of  the  compound  melting  under  decomposition  with  each 
component.  The  compound  melts  at  the  temperature  of  the 
horizontal  DC,  in  that  it  decomposes  to  melt  of  concentration  D  and 

1  If  it  could  be  proven  that  the  three  crystalline  varieties  show  limited 
isomorphism,  the  existence  of  the  compound  would  be  established  without 
question. 

2  ZEMCZUZNYJ,  Z.  anorg.  Chem.,  49,  400  (1906). 

3  VOGEL,  Z.  anorg.  Chem.,  48,  319  (1906). 

4  GUERTLER  and  TAMMANN,  Z.  anorg.  Chem.,  49,  93  (1906). 


220 


THE  ELEMENTS  OF  METALLOGRAPHY. 


mixed  crystals  of  concentration  c  (B  crystals  saturated  with  the 
compound  AmBn,  instead  of  pure  B  crystals).  Determination  of 
the  maximum  of  crystallization  periods  along  the  horizontal  DC, 
namely  i,  is  our  only  means  of  ascertaining  the  composition  of  the 
compound,  since  the  eutectic  horizontal  ab  fails  to  reach  as  far  as 


Weight  per  cent  B 
FIG.  85. 

the  concentration  of  the  compound  (see  below).  The  uncertainty 
associated  with  an  interpretation  of  experimental  results  in  case  of 
miscibility  in  the  crystalline  state  should  not,  however,  be  over- 
estimated. Trifling  miscibility  in  the  crystalline  condition  is, 
indeed,  always  present  (see  p.  213),  and  is  quite  unimportant.  In 
general,  on  consideration  of  the  cases  shown  in  Figs.  85  and  86,  we 
are  inclined  to  assume  that  a  compound  AmBn  exists  — largely  by 
reason  of  the  enhanced  simplicity  and  rationality  of  characteriza- 
tion along  these  lines  —  and  to  consider  this  assumption  better 
grounded  in  proportion  as  the  observed  miscibility  is  smaller,  i.e., 
as  the  gaps  in  miscibility  are  larger.  Furthermore,  in  the  event  that 
the  composition  of  the  questionable  compound  in  the  given  case 


TWO  COMPONENT   SYSTEMS. 


221 


can  be  represented  by  a  simple  formula,  we  are  possessed  of  sub- 
stantial evidence  supporting  this  view.  Similar  reasoning  applies 
to  the  relations  shown  in  Figs.  80  and  82.  One  would  be  inclined  to 
conclude  that  compounds  exist  at  the  points  D  and  C,  respectively, 
in  case  these  concentrations  should  correspond  to  simple  formulas. 


Weight  jper  cent  B 
FIG.  86. 


100 


Determination  of  the  composition  of  those  compounds  which  are 
indicated  in  the  diagrams  given  in  Figs.  80, 82  and  86  is  based  upon 
the  hypothesis  that  the  respective  compound  is  capable  of  dissolv- 
ing only  one  component  appreciably  in  the  crystalline  state  (the 
component  A  in  the  present  instances),  whereby  the  composition 
of  mixed  crystals  composed  of  AmBn  saturated  with  B  practically 
corresponds  to  the  formula  AmBn.  The  portion  of  the  solubility 
curve  of  the  two  crystalline  varieties  AmBn  and  B  which  is  adjacent 
to  the  concentration  of  the  compound  must,  therefore,  run  verti- 


222 


THE  ELEMENTS  OF  METALLOGRAPHY. 


cally,  provided  no  increase  in  solubility  takes  place  as  the  tem- 
perature falls.  Experimental  evidence  in  this  direction  is  not 
readily  obtained,  for  reasons  given  on  p.  202. 

§5.  THE  LIQUID  STATE  is  CHARACTERIZED  BY  INCOMPLETE 
MISCIBILITY;  THE  CRYSTALLINE  STATE  BY  COMPLETE  OR 
INCOMPLETE  MISCIBILITY. 

Since  the  miscibility  of  substances  is,  in  general,  greater  in  the 
liquid  state  than  in  the  crystalline  state,  this  case  will  occur  rather 
infrequently.  If  we  assume  that  complete  isomorphism  obtains  as 


Weight  per  cent  B 
FIG.  87. 


100 


regards  the  crystalline  state,  we  may  use  the  lower  portion  of  Fig. 
84  in  representing  this  case  since  here,  as  in  the  other  instance, 
limited  miscibility  occurs  in  the  state  which  is  stable  at  the  higher 
temperature.  We  must,  then,  make  a  further  assumption  that  the 
two  curves  which  enter  at  a  and  6,  respectively,  from  above  are 
branches  of  the  solubility  curve  of  the  melt.  At  the  temperature 
of  the  horizontal  bac,  the  B-rich  layer  of  concentration  a  is  resolved 
into  mixed  crystals  of  composition  c  and  A-rich  melt  of  concen- 
tration b. 


TWO  COMPONENT  SYSTEMS.  223 

A  case  in  which  limited  miscibility  characterizes  both  crystalline 
and  liquid  states  is  represented  in  Fig.  87.  This  is  completely 
analogous  to  the  case  given  in  Fig.  49,  but  here  saturated  mixed 
crystals  of  B  in  A  and  of  A  in  B  separate,  instead  of  the  pure  sub- 
stances A  and  B,  respectively.  Finally,  the  reader  is  referred  to  the 
discussion  of  an  additional  case  by  TAMMANN.* 

§  6.   THE  SEPARATION  OF  CRYSTALLINE  VARIETIES  WHICH  ARE 
NOT  COMPLETELY  STABLE. 

A.    The  System  :  Antimony-Cadmium. 

We  have  assumed  in  all  previous  discussion  that  every  system 
treated  has  represented  equilibrium  conditions,  i.e.,  that  the 
systems  on  being  left  alone  for  a  length  of  time  would  not 
undergo  change.  During  the  study  of  the  system  Sb-Cd,  phe- 
nomena due  to  non-realization  of  this  assumption  were  observed. 
TREiTSCHKE2  obtained  two  different  melting-point  diagrams, 
according  to  whether  the  melt  was  inoculated  at  the  proper 
time  on  cooling,  or  allowed  to  crystallize  spontaneously.  Fig.  88a 
gives  the  diagram  obtained  by  the  aid  of  inoculation,  and  con- 
sequently refers  to  equilibrium  between  perfectly  stable  crys- 
talline varieties.  We  read  at  once  from  the  diagram  that  Sb 
and  Cd  unite  to  form  a  compound  of  the  formula  SbCd  which 
melts  at  about  460  degrees  and  fails  to  mix  in  the  crystalline 
state  with  either  of  its  components  (concerning  an  accessory  con- 
dition, which  has  not  been  completely  explained,  reference  should 
be  made  to  the  original  paper).  In  particular,  we  note  that  this 
compound  forms  an  eutectic  with  antimony  at  455  degrees  (B  — 
containing  60  per  cent  Sb).  This  compound  appears  in  the  sections 
of  the  reguli  in  the  form  of  long  needles. 

If  inoculation  is  omitted,  the  branch  AB,  along  which  primary 
separation  of  antimony  occurs,  is  realized  at  lower  temperatures 
and  higher  cadmium  concentrations,  namely,  as  far  as  the  point 
B'  (Fig.  88b)  corresponding  to  408  degrees  and  54  per  cent  Sb.  A 

1  TAMMANN,  Ann.  der  Phys.  (4)  19,  421  (1906). 

2  TREITSCHKE,  Z.  anorg.  Chem.,  50,  217  (1906).      The  results  given  in  a 
preliminary  communication  to  the  Jour.  Russ.  Phys.  Chem.  Soc.,  37,  580, 
(1905),  by  Kurnakow  and  Konstantinow  appear  to  generally  agree  with 
those  of  Treitschke. 


224 


THE  ELEMENTS  OF  METALLOGRAPHY. 


compound  C',  which  melts  at  424  degrees,  separates  primarily  in 
concentrations  between  54  and  30  per  cent  Sb.  This  compound  is 
miscible  with  antimony  in  the  crystalline  state  in  all  proportions 
up  to  the  concentration  B'.  Its  probable  formula  is  Sb2Cd3.  It 
must  be  an  unstable  compound,  for  it  is  clear  that  a  melt  which 


Sb                                     Weight  per  cent  Antimony                                         Cd 

650° 

00       90        80         70         60         50         40         30         20         10          ( 

650° 

A 
\. 

8$ 

?d 

600° 

\ 

R00° 

500° 

\ 

\ 

500° 

\ 

.  \ 

B^-£. 

^ 

1  .. 

N 

\ 

400° 

\ 

400" 

§ 

X 

Sb  + 

Eutecti 

•f 

SbCd 

& 

S 

E 

1 

\ 

n  •/ 

300° 

\ 

s^ 

300 

•    • 

. 

. 

\/  ' 

bo 

•"•    j. 

\       ^     o 

1    0 

i 

tf 

4 

i 

J. 

200° 

200° 

0 

n 

150° 

P 

i  I 

q 

150° 

100       90         80         70        60         50        40         30         20         10         0 

Sb                                     Weight  per  cent  A  ntimony                                        Cd 

FIG.  88a.    Fusion  Diagram  of  the  stable  System  Antimony-Cadmium 
according  to  Treitschke. 

has  been  cooled  as  far  as  the  branch  B'C',  for  example,  must  be 
super-cooled  with  respect  to  the  compound  SbCd  —  separating  at 
a  higher  temperature.  On  this  account,  the  spontaneous  evolu- 
tion of  considerable  heat  is  noted  on  further  cooling  —  due  to 
decomposition  of  the  compound  Sb2Cd3  (or  its  mixed  crystals), 
with  formation  of  the  stable  compound  SbCd  (whereby  the  tern- 


TWO  COMPONENT  SYSTEMS. 


225 


perature  may  rise  momentarily  by  as  much  as  50  degrees).  There 
was  no  regularity  in  the  temperature  at  which  this  sudden  tem- 
perature elevation  began  —  noted  in  the  diagram  by  crosses. 

It  was  found  possible  to  bring  the  unstable  compound  within  a 
sphere  of  low  reaction  velocity  by  quenching  the  reguli  at  400 


s 

1( 
650° 

600C 

500° 
400° 

300° 

200° 

150° 
11 

Sb 

b                                         Weight  per  cent  Antimony                                  .    /- 
)0          90           80           70           60           50          40           30           20           10           ( 

650° 
600° 

500° 
400° 
300° 

200° 

150° 

i 

y<* 

<^ 

Sb2 

Cds 

\ 

\ 

£6 

\ 

V 

, 

cf 

**~~ 

£ 

6+6 

11 

x 

xMixed  Crystt 

Sb2Cd 

, 

X. 

. 

1 

T 

I 

O 

T 

n 

)0         90,          80           70           60           50          40          30           20          10           C 
Weight  per  cent  Antimony                                          £ 

FIG.  88b.     Fusion  Diagram  of  the  unstable  System  Antimony-Cadmium 
according  to  Treitschke. 

degrees  in  water.  In  this  way,  the  above  reaction  was  practically 
prevented  (see  p.  147).  Reguli  containing  42,  48,  and  52  per 
cent  Sb,  which  were  treated  as  above,  revealed  large  homogene- 
ous polygons  of  the  compound  Sb2Cd3,  or  of  the  mixed  crystals 
Sb2Cd3  +  Sb,  when  viewed  under  the  microscope. 


226  THE  ELEMENTS  OF  METALLOGRAPHY. 

The  equilibrium  curves  shown  in  Figs.  88a  and  88b  may  be 
entered  in  a  single  coordinate  system,  whereby  one  melting- 
point  diagram,  giving  both  the  stable  and  unstable  conditions, 
is  obtained.  The  points  A  and  A',  corresponding  to  the  melt 
ing  point  of  antimony,  will  then  coincide,  as  will  the  branch 
AB  with  its  length  along  the  branch  A'B',  since  both  correspond 
to  separation  of  the  same  crystalline  variety,  namely,  antimony. 
Nevertheless,  the  curve  branch  BCD,  referring  to  the  stable 
compound,  cuts  the  branch  AB  at  a  higher  temperature  than 
does  the  branch  B'C',  referring  to  the  unstable  compound, 
thereby  concealing  the  latter  branch,  in  accord  with  the  fact  that 
B'C'  represents  the  equilibrium  curve  of  a  supercooled  system. 

Phenomena  quite  analogous  to  the  above  are  encountered  in 
the  system  Zn-Sb,  according  to  ZEMCzuzNYJ1. 

B.    The  System:  Iron-Carbon. 

The  above  description  of  phenomena  attending  the  solidifica- 
tion of  Sb-Cd  alloys  will  serve  as  a  key  to  the  interpretation  of 
the  iron-carbon  system.  According  to  the  conception  of  HEYN,2 
we  have  here  conditions  of  varying  stability,  so  that  the  complete 
melting-point  diagram  of  the  iron-carbon  alloys  may  be  regarded 
in  a  composite  sense,  i.e.,  as  resulting  from  the  superposition  of 
two  separate  diagrams,  one  corresponding  to  completely  stable 
conditions,  and  the  other  to  unstable  conditions.  The  tendency 
towards  supercooling  is,  nevertheless,  much  more  marked  in  this 
case  than  in  the  previously  considered  case  of  antimony-cadmium 
alloys. 

Great  interest  has  always  followed  the  investigation  of  the  con- 
stitution of  iron-carbon  alloys,  obviously  for  the  especial  reason 
that  these  alloys  are  by  far  the  most  important  of  all  alloys  from 
a  technical  standpoint,  but  in  some  degree  due  to  the  fact  that 
the  interpretation  of  certain  observed  processes  has  proven 
unusually  difficult.  The  development  of  Metallography  has  been 
most  vitally  associated  with  the  progressive  investigation  of 
the  iron-carbon  system.  SORBY  and  MARTENS  brought  the 
microscope  into  the  service  of  Metallography  in  this  way.  A 

1  ZEMCZUZNYJ,  Z.  anorg.  Chem.,  49,  384  (1906) 

2  HEYN,  Z.  Electrochemie,  10,  491  (1904). 


TWO  COMPONENT  SYSTEMS.  227 

few  steps  in  advance,  the  names  of  OSMOND  and  ROBERTS-AUSTIN 
are  especially  prominent  in  connection  with  the  systematic  exper- 
imental realization  of  the  melting-point  diagram.  The  extension 
of  our  theoretical  conceptions  of  observed  phenomena,  largely  due 
to  LECHATELIER,  OSMOND,  and  ROBERTS-AUSTIN,  has  kept  pace 
with  the  progressive  accumulation  of  knowledge  relating  to 
actual  facts.  It  meant  further  progress  in  the  former  con- 
nection, when  ROOZEBOOM,  intent  upon  fathoming  the  mutual 
relationship  of  iron  and  carbon,  studied  the  processes  of  forma- 
tion of  mixed  crystals  from  their  melts,  both  theoretically  and 
experimentally,  and  applied  his  conclusions  to  the  crystallization 
processes  of  iron-carbon  alloys.  The  melting-point  diagram 
which  he  evolved1  on  the  basis  of  Roberts- Austin's  experimental 
data  appears,  however,  somewhat  at  variance  with  the  facts 
relative  to  general  stability  relations,  an  issue  first  pointed  out 
by  Heyn  (1.  c.).  Recently  WusT,2  CHARPY,S  and  BENEDICKS* 
have  testified  to  results  of  the  same  description.  The  main 
points  according  to  Heyn  are  presented  in  the  following  dis- 
cussion. We  take  occasion  to  remark,  in  common  with  Heyn, 
that  these  relations  are  in  no  wise  to  be  considered  as  completely 
substantiated.  Consideration  of  certain  phenomena  is  omitted 
in  the  interest  of  simplicity. 

1.  THE  INCOMPLETELY  STABLE  SYSTEM:  IRON-CARBON. — The 
melting-point  diagram  given  in  Fig.  89a  represents  the  crystalli- 
zation processes  which  occur  under  normal  rate  of  cooling  in  such 
iron-carbon  alloys  as  do  not  exceed  4.2  per  cent  in  carbon  content 
—  corresponding  to  the  point  B'.  If  we  assume  with  Heyn  that, 
in  spite  of  normal  cooling,  this  diagram  in  part  represents  con- 
ditions which  are  not  completely  stable,  but  more  or  less  super- 
cooled, then  we  must  concede  to  the  iron-carbon  alloys  a  marked 
tendency  towards  solidification  and  subsequent  persistence  in  the 
form  of  unstable  crystalline  varieties.  Characteristic  of  the  melt- 
ing-point diagram  shown  in  Fig.  89a  is  the  (incompletely  stable) 

1  ROOZEBOOM,  Z.  phys.  Chem.,  34,  437  (1900). 

3  WiteT,  WuLLNER-Festschrift,  Leipzig,  1905,  240;  Metallurgie,  31 
(1906). 

3  CHARPY,  Compt.  rend.,  141,  948  (1905). 

4  BENEDICKS,   Metallurgie,   3,   393   (1906).      This    has  also  appeared   in 
pamphlet  form,  Halle  a.  S.    1907) 


228 


THE  ELEMENTS   OF   METALLOGRAPHY. 


iron-carbon  compound  of  formula  Fe3C  (corresponding  to 
6.7  %  C).  This  iron  carbide,  called  cementite  by  metallurgists, 
possesses  no  capacity  for  dissolving  iron  in  the  crystalline  state. 
It  exhibits  very  considerable  hardness  and  resistance  to  the  action 
of  etching  agents,  whereby  it  may  be  readily  separated  from  any 
slightly  resistant  associated  material  by  treatment  with  dilute 


900 


800° 
F 

700° 


/  +  Cementite 

U 


H 


Pearlite-r 
Cementite 


12345678 
Weight  per  cent  Carbon 

FIG.  89a.    Fusion  Diagram  of  Iron-Carbon  Alloys.    The  incompletely  stable 

system. 


acids.  It  dissolves  in  concentrated  acids  with  evolution  of  hy- 
drogen and  hydrocarbons.  There  has  been  no  doubt  of  its  exist- 
ence since  the  investigations  of  MYLIUS,  FOERSTER  and  ScnoENE.1 
The  following  details  may  be  recognized  in  Fig.  89a.  The 
melting  point  of  pure  iron,  A,  is  1510  degrees.  Iron  undergoes 

1  MYLIUS,  FOERSTER  and  SCHOENE,  Z.  anorg.  Chem.,  13,  38  (1896). 


TWO  COMPONENT  SYSTEMS.  229 

two  polymorphous  transformations  on  cooling.  The  non-mag- 
netic f  form,  which  is  stable  at  the  highest  temperatures,  changes 
at  890  degrees  (at  the  point  E)  into  the  /?  form,  which  is  also  non- 
magnetic. At  770  degrees  (at  the  point  F)  heat  is  again  liberated, 
owing  to  transformation  of  the  /?  form  into  the  magnetic  a  form, 
which  is  stable  at  lower  temperatures.  Pure  a  iron,  in  its  role  of 
structure  element  in  solid  alloys,  bears  the  name  ferrite.  All 
polymorphous  modifications  of  iron  crystallize  in  the  isometric 
system.  Primary  separation  of  iron  in  the  form  of  mixed  crystals 
takes  place  along  the  curve  AB'.  Their  composition  is  indicated 
by  the  curve  Aa'.  Primary  separation  of  cementite  is  represented 
by  the  branch  D'B'  and  is  characterized  by  the  absence  of  mixed 
crystal  formation,  as  previously  noted.  Since  the  tendency 
toward  formation  of  incompletely  stable  crystalline  varieties 
becomes  very  prominent  in  the  case  of  alloys  of  appreciably  higher 
carbon  content  than  corresponds  to  B',  the  course  of  this  branch 
of  the  curve  is  uncertain,  and  has  never  been  determined  for 
concentrations  near  that  of  pure  cementite  (corresponding  to  df). 
The  concentration  of  the  point  B'  is  approximately  4.2  per  cent; 
its  temperature,  approximately  1130  degrees.1  Mixed  crystals 
of  concentration  between  Oanda'  (  =  approximately  2.1%  C)  are 
known  as  martensite  (in  honor  of  A.  Martens)  in  their  role  of 
structure  element  in  solid  alloys. 

When  crystallization  along  the  horizontal  a'E'd!  has  ended, 
the  alloy  is  entirely  solid  and  consists  of  a  mixture  of  saturated 
carbon-rich  martensite  crystals  of  the  composition  a',  on  the  one 
hand,  and  pure  cementite  crystals  of  the  composition  d',  on  the 
other  hand.  The  diagram  shows  which  of  these  constituents 
separates  primarily  in  the  different  cases.  The  relative  amounts 
of  eutectic  B'  are  given  by  verticals  upon  the  horizontal  a'B'd'. 
The  capability  of  iron  to  dissolve  cementite  in  the  crystalline 
state  decreases  with  the  temperature.  Consequently,  a  sepa- 
ration of  cementite  takes  place  along  the  branch  a'G.  Cementite 
which  has  separated  primarily  in  the  pure  condition  suffers  no 
subsequent  change  in  composition,  as  shown  by  the  vertical  d'H. 
We  have  already  noted  the  polymorphous  transformations  of 
iron  which  take  place  at  E  =  890  degrees,  and  at  F  =  770 
degrees.  The  diagram  shows  that  f  iron  is  capable  of  forming 
1  Compare  WUST,  CHARPY,  and  BENEDICKS,  1.  c. 


230  THE  ELEMENTS   OF   METALLOGRAPHY. 

solid  solutions1  (even  though  they  are  not  completely  stable 
with  certain  amounts  of  cementite.  This  occurs  at  temperatures 
below  E,  the  transformation  point,  as  well  as  in  the  region  of  higher 
temperature,  where  pure  ?  iron  is  stable.  We  will  now  assume,  on 
account  of  simplicity,  that  /?  and  a  iron  possess  no  appreciable 
capability  for  dissolving  carbon.2  Under  this  assumption,  viz., 
if  /?  crystals  separate  in  a  pure  state  from  solid  solutions  of  cemen- 
tite and  iron,  the  temperature  of  separation  of  these  /?  crystals 
in  other  words,  the  transformation  temperature  of  f  iron  to  /?  iron, 
must  decrease  along  El  as  the  carbon  content  increases  —  as  far 
as  the  temperature  /  =  770  degrees,  at  which  the  pure  /?  crystals 
become  transformed  into  a  crystals.  Thus,  a  change  in  stability 
occurs  in  concentrations  between  F  and  /,  in  that  the  /?  crystals, 
which  have  separated  thus  far  become  transformed  at  the  con- 
stant temperature  of  the  horizontal  FI  into  a  crystals,  which  now 
constitute  the  stable  modification.  The  condition  that,  from  now 
on,  a  iron  must  separate  from  the  solid  solution,  "7-  iron-cemen- 
tite, "  is  made  evident  by  an  abrupt  change  in  the  direction  of  the 
transformation  curve  at  7.  We  encounter  conditions  which  are 
closely  analogous  to  those  of  eutectic  crystallization  at  the  point 
G  where  the  two  curves  EIG  and  a'G  meet.  The  solid  "solution 
of  cementite  and  iron"  (=  martensite)  is  at  this  temperature 
saturated  with  cementite  as  well  as  with  a  iron.  Consequently, 
on  further  abstraction  of  heat,  there  occurs  simultaneous  sepa- 
ration of  both  crystalline  varieties  in  such  proportions  that  the 
concentration  of  the  solid  solution  is  not  altered.  The  temper- 
ature remains  constant  until  the  martensite  of  concentration  G 
has  been  completely  transformed  into  an  eutectic  mixture  oi  a 
iron  and  cementite.  This  eutectic,  which  shows  a  beautiful 
lamellar  structure,  is  called  pearlite.  The  point  G  corresponds  to 
0.85  %  C  and  690  degrees.  The  eutectic  horizontal  reaches  from 
K  to  H,  while  the  relative  amounts  of  eutectic  have  their  maximum 
at  G}  and  decrease  lineally  on  both  sides  to  zero.  In  case  crystal- 

1  See  p.  163. 

2  Compare,   however,  the  investigation  of  Benedicks  in  this  connection 
(Recherches  phys.   et  phys.-chim.   sur   1'acier  au  carbone,   Upsala,    1904), 
according  to  which  /?  iron  may  dissolve  0.27  per  cent  hardening  carbon.     No 
distinction    between    temper   carbon    and    carbide-carbon    is    made  above. 
The  form  in  which  carbon  is  to  be  found  by  preference  in  solution  in  iron 
cannot  be  given  with  certainty.     Compare  v.  Jiiptner,  Ber.,  39,  2385  (1906). 


TWO  COMPONENT  SYSTEMS.  231 

lization  has  proceeded  as  described  above,  cold  alloys  of  concen- 
trations between  0  and  0.85  %  C  consist  of  ferrite  (a  iron)  and 
pearlite  (eutectic  G) ;  the  alloy  of  concentration  0.85  %  C  consists 
of  pearlite;  and  those  between  0.85  and  6.7  %  C  consist  of  cem- 
entite  (Fe3C)  and  pearlite. 

Now,  it  is  possible  by  means  of  sufficiently  rapid  cooling  to 
retard  the  processes  which  take  place  along  EIGa'.  We  are  there- 
fore in  possession  of  a  method  for  realizing  conditions  which  are 
even  more  unstable  than  those  given  in  our  diagram. 

2.  THE  COMPLETELY  STABLE  SYSTEM:  IRON-CARBON.  —  Accord- 
ing to  Heyn  (1.  c.),  the  following  experimental  facts  testify  in  favor 
of  an  assumption  that  the  diagram  which  we  have  discussed  above, 
in  part  represents  incompletely  stable  conditions: 

(1)  Alloys  appreciably  greater  in  carbon  content  than  corre- 
sponds to  the  point  B'  =  4.2  %,  contain,  on  solidification,  not  only 
cementite,  but  primarily  separated  graphite  as  well.     The  amount 
of  graphite  increases  as  the  rate  of  cooling  decreases. 

(2)  If  iron-carbon  alloys  are  exposed  for  a  sufficiently  long 
period  (some  days)  to  a  high  temperature  (about  that  of  red  heat), 
there  results  on  cooling  (at  least  in  part)  a  mixture  of  practically 
pure  iron  and  carbon.     Carbon  separated  in  this  manner  is  called 
"hardening  carbon"    by    metallurgists.      It    closely    resembles 
graphite  in  its  properties,  and  is  possibly  identical  with  the  lat- 
ter.    (Graphite  and    hardening  carbon  constitute  the  residue  of 
uncombined  carbon  obtained  on  treating  the  alloys  with  acids.) 

We  conclude  from  these  observations  that  the  iron-carbon 
system  which  is  stable  at  red  heat  consists  of  pure  iron  and  pure 
carbon.  Now,  on  crystallization  of  iron-carbon  alloys,  iron  never 
separates  in  the  pure  state,  but  always  in  the  form  of  mixed  crystals. 
One  might  be  inclined  to  attribute  this  phenomenon  to  unstable 
conditions;  nevertheless,  such  appears  improbable,  so  long  as  we 
assume  that  the  liquid  solution  of  carbon  in  iron  exists  in  only  one 
condition  (and  there  is  no  reason  for  believing  otherwise).  For, 
the  melting-point  lowering  which  a  pure  substance  sustains  on 
addition  of  a  second  substance  is  greatest  when  it  (the  solvent) 
crystallizes  out  in  the  pure  state  (see  p.  70).  Thus,  a  curve 
which  corresponds  to  the  equilibrium  between  A  crystals  and 
A  -f  B  melt  will  run  at  a  lower  temperature  in  all  concentrations 
than  a  curve  which  corresponds  to  the  equilibrium  between  A  -f  B 


232 


THE  ELEMENTS   OF   METALLOGRAPHY. 


mixed  crystals  and  A  +  B  melt.  Hence,  as  long  as  separation  of 
a  given  crystalline  variety  both  in  the  pure  state  and  in  the  form 
of  mixed  crystals  is  possible,  and  as  long  as  melt  and  the  crystals 
separating  from  it  are  in  equilibrium,  the  pure  form  will  be  un- 
stable. On  this  account,  we  prefer  to  regard  primarily  separated 
iron  in  the  form  of  mixed  crystals  as  stable.  Fig.  89b  is  drawn 


-  1600° 
1500C 
1400° 
1300° 

I  1200° 

1 1100° 

p^ 

1000' 
900° 
800' 
700C 


Mixed 
Crystals 


Graphite 
+Melt 


/x          SaVd  Mixed  Crystals  +  Graphite 
y-Iron+Graphite 


E 


-Iron+ Graphite 


a-Iron  (Ferrite)  4-  Graphite 


12345678 
Weight  per  cent  Carbon 

FIG.  89b.    Fusion  Diagram  of  Iron-Carbon  Alloys.    The  completely 
stable  system. 

to  this  effect  with  due  regard  for  Heyn's  views.  In  this  com- 
pletely stable  system,  iron  separates  primarily  in  the  form  of  mixed 
crystals  in  concentrations  from  0  to  B  along  the  curve  branch  AB. 
The  composition  of  these  mixed  crystals  is  indicated  by  the  branch 
Aa.  The  courses  of  these  two  branches  are  identical  with  those 
of  the  respective  branches  AB'  and  Aa'  of  the  incompletely  stable 
system  (Fig.  89a).  On  the  other  hand,  primary  separation  of 


TWO  COMPONENT  SYSTEMS.  233 

carbon  in  the  completely  stable  system  does  not  occur  in  the 
form  of  cementite,  but  in  the  form  of  graphite.  This  is  repre- 
sented by  the  branch  DB  (Fig.  89b),  which  must  run  at  a  higher 
temperature  than  the  curve  D'B'  (Fig.  89a)  for  all  concentrations. 
According  to  this  conception,  a  completely  stable  iron-carbon 
compound  is  not  existent  within  the  concentration  range  under 
consideration.  If  this  holds  true  for  higher  carbon  concentra- 
tions as  well,  and  if  complete  miscibility  between  iron  and  carbon 
in  the  liquid  state  continues,  DB  must  ultimately  reach  to  the 
melting  point  of  pure  graphite.  However,  nothing  definite  is 
known  relative  to  concentrations  containing  more  than  8%  C. 
*  According  to  the  investigation  of  Charpy  (I.e.),  the  eutectic  point 
B  of  the  completely  stable  system  (Fig.  89b)  lies  about  10  to  15 
degrees  higher  than  the  eutectic  point  B'  of  the  incompletely 
stable  system  (Fig.  89a).  Hence,  we  place  the  temperature  of 
the  point  B  at  1150  degrees  in  round  numbers,  and  its  concen- 
tration at  4%  C.  The  concentration  of  the  stable  saturated 
mixed  crystals  a  (iron,  saturated  with  graphite)  is  about  2%  C. 
When  the  temperature  has  fallen  to  that  of  the  horizontal  aBd 
(=  1150  degrees),  all  of  the  material  crystallizes,  and  after  crystal- 
lization the  alloys  of  concentrations  between  0  and  a  consist  entirely 
of  mixed  crystals,  all  of  which,  if  crystallization  has  proceeded  in 
ideal  manner,  possess  the  composition  of  the  original  alloy.  At 
higher  concentrations,  the  alloys  contain  two  structure  elements, 
namely,  saturated  mixed  crystals  a,  on  the  one  hand,  and  graphite, 
on  the  other  hand.  According  to  the  concentration  in  question, 
either  one  or  the  other  of  these  constituents  appears  primarily  as 
well  as  in  the  eutectic.  The  relative  amounts  of  eutectic  (Mixed 
crystals  a  +  Graphite)  are  indicated  in  the  usual  manner  by  verticals 
erected  upon  the  horizontal  aBd.  Now,  as  we  are  well  aware,  the 
mutual  solubility  of  substances  decreases  in  general  with  the  tem- 
perature. Therefore,  the  saturated  mixed  crystals  a  will  separate 
carbon  (not  in  the  form  of  cementite,  as  in  the  incompletely  stable 
system,  but  in  the  pure  form)  on  further  cooling.  We  now  con- 
form to  Heyn's  conception  by  assuming  a  very  rapid  decrease  in  the 
solubility  of  carbon  as  the  temperature  falls,  such  that  it  becomes 
practically  zero  at  about  1000  degrees  (the  point  X).  This  may 
be  represented  by  the  curve  aX.  This  essentially  hypothetical 
curve  stands  in  recognition  of  the  assumption  that  the  iron- 


234     .  THE  ELEMENTS   OF   METALLOGRAPHY. 

carbon  alloys  existing  below  X  (=  1000  degrees)  are  stable  only 
in  the  form  of  pure  iron  and  pure  carbon  (graphite  or  hardening 
carbon).1  Under  normal  cooling  conditions,  the  curve  aX  is 
invariably  overstepped.  If,  however,  an  alloy  is  held  several  days 
at  as  high  a  temperature  as  is  possible  without  exceeding  X  (this 
is  done  in  tempering),  at  least  a  partial  realization  of  the  separa- 
tion required  by  our  diagram  is  effected. 

Since,  according  to  the  diagram,  all  alloys  existing  below  the 
temperature  of  X  (=  approximately  1000  degrees)  must  have 
become  resolved  into  pure  iron  and  pure  carbon,  the  transfor- 
mation temperatures  of  y  iron  and  /?  iron,  respectively,  cannot  be 
altered  by  the  presence  of  carbon  in  the  original  alloy.  Hence, 
we  draw  horizontals  through  the  points  E  =  890  degrees  and 
p  =  770  degrees  (see  p.  214)  in  order  to  indicate  constant 
transformation  temperature  of  iron  throughout  the  whole  concen- 
tration range.  Thus,  we  see  that  the  completely  stable  iron-car- 
bon alloys  must  consist  exclusively  of  pure  iron  and  pure  carbon 
at  temperatures  below  1000  degrees,  provided  our  melting-point 
diagram  is  accurate.  Complete  realization  of  the  stable  condition 
is,  nevertheless,  invariably  precluded,  as  previously  mentioned, 
by  the  inherent  tendency  of  these  alloys  towards  supercooling. 

3.  THE  COMPLETE  SYSTEM:  IRON-CARBON. — The  fact  that 
very  varied  properties  may  be  imparted  to  an  iron-carbon  alloy 
of  a  given  percentage  composition  finds  its  explanation  in  the  vari- 
able stability  of  the  system.  This  diversity  is  clearly  revealed 
on  combining  both  diagrams.  Fig.  89c  shows  such  combination 
(omitting  several  complications,  such  as  verticals  upon  theeutectic, 
and  the  horizontal  through  E  and  F).  The  equilibrium  curves 
which  correspond  to  stable  conditions  are  drawn  in  dotted  lines, 

1  BENEDICKS  (1.  c.)  assumes  a  less  rapid  decrease  in  the  solubility  of  car- 
bon in  iron  with  the  temperature  on  the  basis  of  experiments  by  MANNES- 
MANN  and  CHARPY  and  GRENET.  The  temperature  field  within  which  the 
alloys  are  capable  of  resolution  into  pure  iron  and  carbon  is  then  placed 
below  800  degrees  (at  about  750  degrees).  An  experiment  by  WUST  (Metallur- 
gie,  3,  11  (1906)),  appears  to  contradict  this,  in  that  a  partial  resolution  of 
iron,  containing  3.8  per  cent  C.,  into  pure  iron  and  hardening  carbon  was 
effected  at  the  high  temperature  of  980  degrees.  We  shall  be  unable  to 
affirm  more  positively  on  this  point  until  it  has  been  decided  by  experiment 
whether  or  not  complete  resolution  of  the  iron-carbon  alloys  into  iron  and 
carbon  may  actually  occur  and,  if  so,  at  what  temperature. 


TWO  COMPONENT  SYSTEMS. 


235 


since  they  have  not  been  realized  thermally,  and  are,  consequently, 
to  a  certain  extent  hypothetical.  In  contradistinction,  the  equi- 
librium curves  which  are  drawn  in  full  lines  represent  the  "  realiz- 
able," incompletely  stable  conditions.  Both  diagrams  agree  only 
with  respect  to  the  points  A,  E,  and  F  and  the  equilibrium  curves 
Aa  and  AB,  which  latter  are,  for  this  reason,  drawn  in  alternating 


1234567 
Weight  per  cent  Carbon 

FIG.  89c.    Fusion  Diagram  of  Iron-Carbon  Alloys. 
The  complete  system. 

full  and  dotted  lines.  Where  the  two  fail  of  agreement,  curves 
drawn  in  full  lines  must  represent  supercooled  conditions  and 
therefore  lie  below  the  dotted  lines.  In  accordance  with  the 
above  exposition,  the  following  constituents  may  be  found  in  solid 
iron-carbon  alloys  at  ordinary  temperature. 

(1)  Under  absolutely  stable  conditions  (Fig.  89b):  pure  a  iron 
(=  ferrite)  and  graphite  (or  "  hardening  carbon")- 


236  THE  ELEMENTS   OF   METALLOGRAPHY. 

(2)  Under  incompletely  stable  conditions  (Fig.  89a) : 

(a)  ferrite  and  pearlite  (eutectic  of  ferrite  and  cementite), 

(b)  pearlite  alone, 

(c)  pearlite  and  cementite. 

(3)  Under  the  least  stable  condition,  i.e.,  when  the  curve  EJGa' 
has  been  overstepped:  martensite  (mixed  crystals  of  7-  iron  and 
cementite),  with  or  without  cementite. 

Owing  to  the  possibility  that  the  condition  of  stability  may  vary 
in  the  same  alloy  at  different  points  —  that,  in  effect,  the  constitu- 
ents enumerated  under  1,  2,  and  3  above  may  appear  simultane- 
ously and  in  changing  proportions  —  we  are  in  a  position  to  alter 
the  properties  of  the  iron-carbon  alloys  within  rather  wide  limits 
without  altering  their  composition.  Thus,  the  difference  between 
gray  and  white  pig  iron  consists  in  that  the  former  contains  a 
greater  or  lesser  amount  of  graphite,  while  the  latter  contains 
chemically  combined  carbon  only.  Since  pig  iron  contains  more 
than  1.8%  C,  the  white  variety  must  consist  exclusively  of  cemen- 
tite and  pearlite  (martensite  also,  on  occasion),  and  the  white 
variety  of  these  same  materials,  together  with  graphite.  The  latter, 
variety  alone  will  leave  a  residue  of  carbon  on  treatment  with  acids, 
since  chemically  combined  carbon  is  always  liberated  in  the  form 
of  hydrocarbons. 

If  the  pig  iron  contains  no  silicon,  it  invariably  solidifies  as  white 
cast  iron,  provided  its  carbon  content  does  not  exceed  4  per  cent. 
Silicon  lessens  the  tendency  toward  supercooling  to  a  greater  or 
lesser  extent,  according  to  the  amount  present.  Pig  iron  of  ap- 
proximately 4  per  cent  carbon  content,  which  also  contains  silicon, 
solidifies  to  the  gray  form  —  containing  graphite  and,  of  course, 
varying  amounts  of  cementite.  In  the  case  of  pig  irons  contain- 
ing a  greater  amount  of  carbon,  i.e.,  exceeding  4  per  cent,  it  is  also 
possible,  even  in  the  absence  of  an  appreciable  quantity  of  silicon, 
to  bring  about  primary  separation  of  graphite  by  slow  cooling.1 
Manganese,  on  the  other  hand,  is  effectual  in  inducing  supercooling. 
Hence,  varieties  of  pig  iron  which  contain  manganese  solidify,  in 
general,  in  the  white  form,  even  when  their  carbon  content  exceeds 
5  per  cent.  Separation  of  carbon  from  samples  of  iron  containing 

1  This,  however,  appears  somewhat  doubtful,  according  to  recent  experi- 
ments by  WUST. 


TWO  COMPONENT  SYSTEMS. 


237 


cementite  on  lengthy  exposure  to  a  temperature  of  bright  redness 
has  already  been  discussed  (p.  231). 

Iron-carbon  alloys  of  1.8  percent  carbon  content  and  less  are 
known  as  steel,  wrought  iron,  etc.  The  diagram  shows  us  that  the 
possibility  of  varying  conditions  in  this  region  is  particularly 
extended,  owing  to  the  presence  of  the  curve  EIGa'.  In  setting 
out  to  prepare  an  iron  of  certain  prescribed  properties,  familiarity 
with  the  diagram,  in  connection  with  knowledge  of  the  properties 
of  the  individual  structure  elements  (see  the  following  table),  is 
of  great  service. 

TABLE  6. 


Hardness. 

Coloring  with  tinc- 
ture of  iodine. 

Behavior  towards 
10  per  cent  sulphuric 
acid  —  cold. 

Ferrite,  Fe 

Softest  structure 
element. 

Very     faint     or 
none  at  all. 

Dissolves  readily 
with    evolution 
of  hydrogen. 

Cementite,  Fe3C. 

Hardest  structure 
element. 

None. 

Fails  to  dissolve. 

Pearlite, 
Fe+Fe3C. 

Medium. 

Inappreciable. 

Dissolves    par- 
tially. 

Martensite, 
mixed  crystals 
of    cementite 
+  7  iron. 

Varying  hardness 
according    to 
C-content.  In- 
variably softer 
than  cementite. 

Yellow  to  brown. 

Dissolves        with 
evolution        of 
hydrogen    and 
hydro-carbons. 

For  example,  if  it  is  desired  to  impart  the  greatest  possible 
hardness  to  an  iron  of  definite  carbon  content,  say  approximately, 
1  per  cent,  the  formation  of  pearlite,  which  is  moderately  soft, 
should  be  hindered.  That  is  to  say,  the  alloy  should  be  con- 
ducted with  all  possible  rapidity  from  the  martensite  field  into 
the  field  of  trifling  reaction  velocity,  where  the  (hard)  martensite 
no  longer  undergoes  transformation  into  pearlite  and  cementite. 
This  process  of  quenching  is  called  hardening.  The  temperature 
at  which  rapid  cooling  should  begin  lies  above  EIGa',  and  may 
be  read  directly  from  the  diagram  when  the  carbon  content  is 
known.  If  the  hardened  steel  is  subjected  to  a  temperature  of 
more  than  200  degrees,  it  is  then  in  a  condition  to  favor  the 


238  THE  ELEMENTS   OF   METALLOGRAPHY. 

resolution  of  martensite  into  ferrite  and  cementite  with  appreci- 
able rapidity  (compare  Heyn,  loc.  cit.,  p.  226).  In  this  manner, 
a  steel  of  greater  hardness  than  is  desired  may  be  tempered 
to  a  lesser  degree  of  hardness  (tempering  of  steel), 

§  7.   SUPPLEMENTARY. 

For  progress  in  our  perception  of  the  nature  of  metallic  alloys 
we  are  primarily  indebted  to  thermal  methods.  In  that  they 
teach  us  concerning  not  only  transient  conditions  encountered, 
but  also  concerning  the  whole  history  of  alloy  formation,  these 
methods  furnish  a  key  to  the  understanding  of  the  ofttimes  com- 
plicated inter-relations  of  the  components.  Nevertheless,  these 
methods  fail  of  results  in  two  cases:  in  the  first  place,  when  the 
reaction  is  accompanied  by  a  very  slight  heat  effect,  and,  in  the 
second  place,  when  the  rate  of  reaction  under  the  given  experi- 
mental conditions  is  so  trifling  that  the  reaction  no  longer  becomes 
regulated  by  flow  of  heat  (p.  10).  For  this  reason,  several  other 
methods  which  have  found  application  in  the  investigation  of 
binary  systems  will  now  be  briefly  treated.  These  methods  come 
under  two  categories:  those  which  are  applicable  to  the  determi- 
nation of  equilibrium  curves,  and  those  which  are  merely  adapted 
to  investigation  of  the  solidified  mixture.  Among  the  latter  is 
included  one  which  has  been  discussed  at  length,  namely,  the 
microscopical  investigation  of  prepared  sections. 

A.    Methods  of  Determination  of  Equilibrium  Curves. 

1.  METHOD  OF  SOLUBILITY  DETERMINATION. — This  method 
is  identical  in  principle  with  the  thermal  method.  While  the 
concentration  of  the  liquid  mixture  is  known  in  the  case  of  the 
thermal  method,  and  we  determine  the  temperature  at  which  it 
begins  to  solidify,  i.e.,  the  temperature  at  which  it  is  in  equilib- 
rium with  a  crystalline  phase,  in  the  present  case  the  composition 
of  the  liquid  mixture  which  is  in  equilibrium  with  this  crystalline 
phase  at  a  given  temperature  is  determined.  This  method  has 
proven  of  service  chiefly  in  the  study  of  equilibria  between  salts 
and  water.  It  is  characterized  by  great  accuracy  and  does  not 
fail  of  application  where  the  heat  effects  are  small.  The  equilib- 
rium may  be  accurately  followed  in  the  practice  of  this  method 


TWO  COMPONENT  SYSTEMS. 


239 


by  allowing  it  to  reach  adjustment  from  both  sides.  Application 
of  the  method  to  metallographical  investigation  is  materially 
hindered  by  the  difficulty  associated  with  the  necessary  separation 
of  crystals  from  mother  liquor  (see  Introd.). 

2.  DILATOMETRICAL  METHODS.  —  Most  substances  contract  on 
solidification.  If  the  specific  volume  of  a  pure  substance  is 
determined  at  different  temperatures,  a  curve  similar  to  that 


Volume 


Volume 


Volume 
FIGS.  90,  91  and  92. 

given  in  Fig.  90  is  obtained.  From  this  curve,  it  is  seen  that  the 
substance  has  solidified  as  a  unit,  in  that  a  marked  decrease  in 
volume  at  the  constant  temperature  of  the  horizontal  be  has 
resulted  during  passage  from  the  liquid  into  the  crystalline 
state.  Fig.  91  gives  the  temperature- volume  curve  of  a  mixture. 
Here,  solidification  has  commenced  at  the  temperature  a  and  has 


240  THE  ELEMENTS   OF  METALLOGRAPHY. 

become  complete  eutectically  at  the  temperature  be.  Fig.  92 
gives  the  temperature- volume  curve  characterizing  solidification 
to  mixed  crystals.  The  crystallization  interval  is  at  be.  Obvi- 
ously, this  method  may  be  used  in  connection  with  all  such  trans- 
formations as  are  accompanied  by  change  in  volume.  Its  use  is 
independent  of  the  magnitude  of  the  heat  effect,  but  is  subject  to 
considerable  experimental  difficulty  at  high  temperatures. 

3.  OPTICAL  METHODS.  —  DOLTER*  has  made  use  of  a  crystalli- 
zation microscope  suited  to  high  temperatures2  in  the  optical 
determination    of    melting    points.     A    small    electrical    heating 
device  is  introduced  between  the  object  table  and  objective  of 
the  microscope.     This  contains  a  cup  in  which  the  powder  to  be 
investigated  is  placed.     The  point  at  which  gold  dust  unites  to 
a  molten  globule  can  be  very  sharply  observed  and  the  correspond- 
ing temperature  accurately  determined  by  means  of  a  thermo- 
element suitably  applied.     This  method  is  particularly  suited  to 
determination  of  the  melting  points  of  such  silicates  as  show 
abnormal  behavior  (probably  on  account  of  high  viscosity  of  the 
melt).8     In  such  cases,  a  rounding  of  the  corners  of  the  crystalline 
particles  would  first  be  noticed,  then  that  of  the  edges,  and, 
finally,   a  complete  collapse,   resulting  in  a  light,  glassy  drop. 
Under  some  circumstances,  a  temperature  difference  of  as  much  as 
100  degrees  characterizes  the  beginning  and  end  of  fusion. 

4.  OTHER  METHODS.  —  Obviously,  any  change  related  to  the 
passage  of  one  form  into  another  may  serve  by  way  of  determi- 
nation  of   the   equilibrium   curve.     In   case   of   certain   metals, 
changes  in  magnetic  permeability  are  prominent  in  this  connec- 
tion.    The  magnetic  properties  of  alloys  may  be  very  different 
from  those  of  their  components.      Thus  an  alloy  of  25  per  cent 
nickel  and  75  per  cent  iron  —  so-called  nickel  steel  —  is,  in  gen- 
eral,   practically    unmagnetic    at    ordinary    temperature.     Con- 
versely,   metals  which    are    themselves  non-magnetic  may  form 
magnetic   alloys.     As  an  example  of  this,  an  alloy  of   Cu,   Mn 
and  Al4  may  be  mentioned.     According  to  WEDEKIND,B  certain 

1  BOLTER,  Z.  Elektrochemie,  12,  617  (1906). 

2  BOLTER,  Phys.-chem.  Mineralogie,  Leipzig,  1905,  p.  130. 

3  See  p.  8. 

4  HEUSLER,    Uber   die    Synthese    ferromagnetischer    Manganlegierungen, 
Marburg,  1904. 

5  WEDEKIND,  Ber.,  40,  1259  (1907). 


TWO  COMPONENT  SYSTEMS. 


241 


definite  compounds  of  manganese  are  carriers  of  ferro-magnetism 
(compare,  in  this  connection,  a  paper  by  WILLIAMS,  Z.  anorg. 
Chem  ,  55,  1  (1907) >. 


B.   Methods  of  Investigation  of  the  Solidified  Mixtures. 

1.  DETERMINATION  OF  THE  SPECIFIC  VOLUME  OF  THE  COM- 
PLETELY SOLIDIFIED  ALLOY.  —  The  specific  volumina  of  mix- 
tures may  be  calculated  according  to  the  rule  of  mixture.  If 
two  substances  form  no  compound  with  one  another,  the  relation 
of  specific  volume  to  concentration  in  the  mixtures  will  be  given 
by  a  straight  line,  provided  no  miscibility  in  the  crystalline  state 


Weight  per  cent  B 
FIG.  93a. 


100 


AmBn 


Weight  per  cent  B 
FIG.  93b. 


100 


occurs  (Fig.  93a).  If,  on  the  contrary,  a  compound  of  concentra- 
tion indicated  by  the  formula  AmBn  is  formed,  this  relation  will 
be  given  by  two  straight  lines  which  coincide  at  the  concentration 
of  the  compound1  (Fig.  93b).  The  use  of  this  method,  which  ap- 
pears, at  first  sight,  free  from  all  objection  in  the  absence  of 
miscibility  in  the  crystalline  state,  has  led  to  many  errors.  The 
method  is  based  upon  the  hypothesis  that  only  two  structure 
elements  are  present  in  the  respective  mixture,  namely,  the  com- 
pound, and  either  of  the  components,  A  or  B.  We  have  seen, 
relative  to  the  discussion  of  the  concealed  maximum,  that  this 
condition  is  not  realized  in  case  of  incomplete  progress  of  the 
reaction  (see  pp.  137,  141).  In  all  such  cases,  this  method  must 

1  MAEY,  Z.  phys.  Chem.,  29,  119,  1899;  38,  292  (1901). 


242 


THE  ELEMENTS   OF   METALLOGRAPHY. 


lead  to  false  conclusions.1  Again,  the  observation  of  KAHLBAUM 
and  STURM2  that  the  specific  weights  of  pure  metals  may  vary 
somewhat  according  to  their  previous  treatment  may  be  cited, 
although  of  relatively  lesser  practical  importance  in  this  con- 
nection. 

2.  DETERMINATION  OF  ELECTRICAL  CONDUCTIVITY.  —  Owing  to 
the  far-reaching  and  exact  investigations  of   MATTHIESSEN,S  we 


Volume  per  cent  B 
FIG.  94a. 


100 


Volume  per  cent  B 
FIG.  94b. 


100 


Volume  per  cent  B 
FIG.  94c. 

have  learned  to  discriminate  between  two  groups  of  alloys,  namely, 
those  whose  specific  conductivity  may  be  approximately  calcu- 
lated from  that  of  their  components  according  to  the  rule  of  mix- 
ture, and  those  in  which  small  additions  of  one  metal  to  the  other 

1  VOGEL,  Z.  anorg.  Chem.,  45,  20  (1905). 

3  KAHLBAUM  and  STURM,  Z.  anorg.  Chem  ,  46,  217  (1905). 

8  MATTHIESSEN,  Pogg  Ann.,  110,  190  (1860). 


TWO  COMPONENT  SYSTEMS.  243 

bring  about  great  decrease  in  conductivity.  On  entering  the  con- 
ductivity in  its  relation  to  volume-concentration  in  a  coordinate 
system,  we  obtain  a  straight  line  for  the  first  group  (Fig.  94a), 
and,  when  both  metals  behave  similarly,  a  curve  of  the  form 
shown  in  Fig.  94b  for  the  second  group.  Five  examples  of  the 
first  type  are  known,  namely,  Sn-Zn,  Sn-Pb,  Sn-Cd,  Pb-Cd  and 
Zn-Cd.  Examples  of  the  second  type  are  Au-Ag,  Au-Cu  and 
Cu-Ni.  LECHATELIERI  was  the  first  to  recognize  the  correct  rela- 
tionship between  constitution  and  conductivity,  notwithstanding 
the  very  limited  perception  of  the  general  constitution  of  metallic 
alloys  then  prevalent.  He  held  the  opinion  that  linear  variation 
of  specific  conductivity  with  volume  concentration  (Fig.  94a) 
ensued  when  the  components  were  disposed  side  by  side  in  the 
crystalline  condition,  and  that  the  frequently  observed  condition 
of  greatly  diminished  conductivity  in  an  alloy  with  respect  to 
that  of  its  components  (Fig.  72b)  was  due  to  mixed  crystal  for- 
mation. This  latter  conclusion  appeared  to  him,  "  seriously  con- 
trovertible  in  the  case  of  alloys  of  iron  with  nickel  and  manganese, 
and  of  silver  with  gold. "  The  occurrence  of  an  angular  maximum 
in  the  conductivity  curve  indicated  the  existence  of  a  compound, 
according  to  LeChatelier. 

RoozEBOOM2  made  the  following  observations  relative  to 
LeChatelier's  inferences.  In  the  first  place,  he  pointed  out  that 
even  in  case  an  alloy  crystallizes  to  a  conglomerate  of  the  pure 
metals,  it  is  not  essential  that  a*  linear  relation  between  conduc- 
tivity and  volume-concentration  obtain.  Consider  two  different 
bars  of  an  alloy  which  is  composed  of  equal  volume  percentages 
of  two  components  which  are  immiscible  in  the  liquid  state  and 
possess  the  respective  specific  conductivities  ^  and  X2.  In  the 
first  bar,  let  the  components  lie  side  by  side  in  the  direction  of  the 
current,  as  shown  in  Fig.  95a.  Then  the  average  conductivity  A 
is  ?  (^i  +  ^2)7  according  to  the  rule  of  mixture.  Now,  let  the 
components  lie  at  right  angles  to  the  direction  of  the  current  in 
the  second  bar,  as  shown  in  Fig.  95b.  Then  the  average  resist- 

1  /I       1 

ivity  -,  as  calculated  from  the  rule  of  mixture,   is 
A 

1  LECHATELIER,  Revue  ge*ne"rale  des  sciences,  6,531,  1895:  Contribution 
I'etude  des  alliages,  Paris,  1901,  p.  446. 

2  ROOZEBOOM,  Die  heterogenen  Gleichgewichte,  II  Teil,  1904,  p.  186. 


244 


THE  ELEMENTS   OF  METALLOGRAPHY. 


2  .  A  /I 

Whence,  A  =          *A  in  this  case,  a  value  consistently  smaller  than 
/!  -j-  X2 

before,  the  difference  being  proportional  to  (^  —  ^2)2.  Rooze- 
boom  concludes  that  neither  the  conductivity  nor  its  reciprocal 
value  can  be  a  linear  function  of  the  volume  concentration,  on 
account  of  the  inherently  irregular  arrangement  of  particles. 

Although  the  above  conclusion  seems  well  founded  in  principle, 
we  must  in  general  expect  an  approximately  linear  relationship 
between  specific  conductivity  and  volume  concentration  in  metallic 


FIG.  95a. 


FIG.  95b. 


\2 

e 

*> 

, 

6 

A 

FIG.  95c. 

conglomerates.  Suppose  we  assume,  for  example,  the  arrange- 
ment given  in  Fig.  95c,  which  must  more  closely  approximate 
the  actual  conditions  than  either  of  the  arrangements  previously 
given.  Calculation  of  the  conductivity  in  such  a  case,  even  under 
the  simplifying  assumption  that  we  are  dealing  with  a  surface 
(thin  plate),  is  a  task  which  cannot  be  solved  in  an  elementary 
manner.  Imagining  the  figure  to  be  divided  into  two  sections 
at  ab,  and  considering  mean  conductivity,  we  conclude  that 
specific  resistivity  is  calculated  according  to  the  rule  of  mixture, 
thus: 


If,  however,  division  is  made  at  cd,  the  same  applies  to  specific 
conductivity,  and  we  obtain: 


A  = 


TWO  COMPONENT   SYSTEMS. 


245 


In  the  first  case,  we  have  presumed  a  division  according  to  Fig.  95d ; 
in  the  second  case,  a  division  according  to  Fig.  95e.  Neither  of 
the  solutions  can  be  considered  rigid,  since  the  assumption  made 
in  the  second  case  that  cd  is  a  line  of  potential  follows  from  the 
assumption  made  in  the  first  case  that  ab  is  a  line  of  current. 
Still,  the  assumption  made  in  the  second  case,  that  the  potential 
is  the  same  at  the  points  c  and  d,  will  be  approximately  realized 


for  a  conductor  having  the  form  of  a  wire,  and  it  thus  appears 
probable  that  a  very  closely  linear  relationship  between  conductiv- 
ity and  concentration  exists.  In  this  connection,  no  allowance 
has  been  made  for  possible  thermo-electric  effects. 

A  second  of  Roozeboom's  objections  rests  upon  the  fact  that, 
even  in  the  case  of  pure  metals,  conductivity  results  depend  upon 
previous  treatment  of  the  material,  such  as  compression,  torsion, 
annealing,  etc.  The  specific  volume  also  varies  along  these  lines, 
as  we  have  seen  on  p.  242,  although  to  a  much  lesser  extent  than 
the  conductivity. 

While  the  fundamental  qualifications  of  the  above  exceptions 
cannot  be  gainsaid,  LeChatelier  appears,  nevertheless,  to  have  hit 
upon  the  truth  of  the  matter  in  its  essentials.  In  particular, 
modifications  of  the  conductivity-concentration  relations  in  metal- 
lic conglomerates,  due  to  the  causes  represented  by  Roozeboom, 
are  not  sufficiently  prominent  to  impair  in  any  way  the  typical 


246  THE  ELEMENTS   OF   METALLOGRAPHY. 

distinction  between  "approximate  lineality"  (Fig.  72a)  and 
"marked  lowering  by  small  additions"  (Fig.  72b).  LeChatelier's 
views  have  recently  been  vigorously  supported  by  GUERTLER,  l  who 
compared  conductivity  diagrams,  drawn  principally  from  Matthies- 
sen's  results,  with  corresponding  melting-point  diagrams,  as  did 
LeChatelier.  Guertler  had  more  accurate  melting-point  diagrams 
and  a  larger  number  of  them  at  his  disposal  than  did  LeChatelier, 
owing  to  immense  progress  in  this  sort  of  work  during  the  inter- 
vening time.  He  differentiates  three  types:  the  two  extreme 
cases,  Fig.  94a,  wherein  no  miscibility  in  the  crystalline  state 
occurs,  and  Fig.  94b,  corresponding  to  complete  miscibility  in  the 
crystalline  state,  with  an  intermediate  case  of  limited  miscibility, 
shown  in  Fig.  94c,  which  is  beautifully  illustrated  by  the  system 
Cu-Co.  In  this  system,  miscibility  marks  the  two  concentration 
ranges,  0  to  a  and  b  to  100,  whence  we  note  a  sharp  decrease  in  spe- 
cific conductivity  from  concentrations  0  and  100  respectively  (the 
pure  metals).  The  specific  conductivity  is  a  linear  function  of  the 
volume-concentration  between  concentrations  a  and  b,  in  which 
interval  the  alloy  represents  a  conglomerate  of  the  two  saturated 
mixed  crystal  varieties  a  and  b.  Cases  covering  the  appearance  of 
compounds  are  represented  by  combination  of  the  three  simple 
types  in  the  well-known  manner. 

Relative  to  the  practical  value  of  conductivity  determinations 
in  studying  the  constitution  of  alloys,  we  note  that  it  is  frequently 
impossible,  on  account  of  brittleness,  to  obtain  alloys  in  the  form 
most  suited  to  accurate  conductivity  determinations,  namely, 
that  of  wire.  Thus,  a  method  for  the  exact  determination  of 
specific  conductivity  in  a  metallic  regulus  just  as  it  leaves  the 
furnace  would  be  of  great  value.  In  using  the  conductivity 
method  for  determination  of  the  composition  of  compounds,  we 
must  be  assured  that  only  two  structure  elements  are  present  in 
the  mixture,  as  was  the  case  relative  to  use  of  the  specific  volume 
method  in  the  same  connection  (see  p.  241). 

It  appears  questionable  to  conclude  that  a  compound  exists  on 
the  basis  of  a  faint  break  in  the  conductivity  curve.  By  way  of 
example,  we  may  cite  Guertler's  first  combination  of  the  con- 
ductivity and  fusion  diagrams  for  the  system  Au-Sn,2  and  his  sub- 

1  GUERTLER,  Z.  anorg.  Chem.,  51,  414  (1906). 

2  GUERTLER,  Z.  anorg.  Chem.,  51,  414  (1906).  Fig.  13. 


TWO  COMPONENT  SYSTEMS.  247 

sequent  correction  of  the  same-2  The  break  a  in  the  conductivity 
curve,1  which,  owing  to  use  of  (no  longer  current)  equivalent 
weights  by  Matthiessen,  would  at  first  sight  appear  to  corre- 
spond to  the  compound  AuSn,  has  lost  all  claim  to  existence 
by  subsequent  correction.2  (It  "may  be  discarded,  being  only 
faintly  perceptible,  without  thereby  working  any  constraint  upon 
Matthiessen's  experimental  figures.")  The  conclusions  from  both 
sources  (conductivity  and  melting-point  diagrams)  still  fail  of 
complete  agreement,  however,  and  an  explanation  of  the  difference 
is  to  be  sought  in  incomplete  progress  of  reaction  (see  p.  134). 
The  only  Au-Sn  compound  which  finds  sharp  and  unaffected  ex- 
pression on  the  conductivity  curve  is  the  compound  AuSn,  which 
had  already  been  described  by  VOGELS  on  the  basis  of  thermal  and 
microscopical  investigation. 

Another  example  which  aids  to  show  that  uncertainties  are  at 
present  connected  with  this  method  is  furnished  by  the  system 
Cu-Sb.  BAiKOW4  has  concluded  on  the  basis  of  his  melting-point 
diagram  that  two  compounds  of  the  respective  formulas,  SbCu2  and 
SbCu3,  exist.  GUERTLERS  found  abrupt  changes  in  direction  on 
the  conductivity  curve  which  he  constructed  from  the  experimental 
measurements  of  KAMENSKY'  at  just  these  concentrations:  at  the 
concentration  SbCu2,  a  sharp  break  directed  upwards,  and,  at  the 
concentration  SbCu3,  a  break  directed  downwards.  KAMENSKY* 
himself  constructed  a  curve  (on  the  basis  of  his  own  experiments, 
carried  out  with  the  induction  balance)  which  exhibited  the  upward 
peak  at  the  concentration  SbCu2  (as  above),  but  located  the  other 
break  at  the  concentration  SbCu4,  and  he,  of  course  unaware  of  the 
melting-point  relations  in  this  system,  drew  the  conclusion  that  two 
alloys  of  "  well-defined"  compositions,  possessing  the  respective 
formulas,  SbCu2  and  SbCu4,  are  existent. 

Regarding  the  system  Cu-Ag  as  well,  it  appears  that  the  manner 
in  which  GUERTLER  7  has  endeavored  to  reconcile  the  evidence  of 

1  GUERTLER,  Z.  anorg.  Chem.,  51,  414  (1906).     Fig.  13. 

2  GUERTLER,  Z.  anorg.  Chem.,  54,  88  (1907).     Fig.  13. 

3  VOGEL,  Z.  anorg.  Chem.,  46,  73  (1905). 

4  Publications  of  the  Czar  Alexander  I  Road  Building  Institute,  St.  Peters- 
burg (1902):   Landolt-Bornstein,  Phys.-chem.  Tables,  III  ed.  (1905),  p.  300. 

5  GUERTLER,  Z.  anorg.  Chem.,  51,  418  (1906). 
B  KAMENSKY,  Phil.  Mag.  (5),  17,  270  (1884). 

7  GUERTLER,  Z.  anorg.  Chem.,  51,  406  (1906). 


248  THE  ELEMENTS   OF   METALLOGRAPHY. 

the  conductivity  diagram  with  that  of  the  melting  point  diagram  is 
not  entirely  beyond  criticism.  The  melting  point  diagram  indi- 
cates existence  of  mixed  crystals  with  a  gap  in  miscibility.  We 
would  thus  expect  a  conductivity  curve  of  the  type,  Fig.  94c.  The 
curve  for  the  case  of  complete  miscibility,  which  is  uniformly  con- 
vex with  respect  to  the  concentration  axis,  is  not  completely  real- 
ized when  a  gap  in  miscibility  occurs,  being  relieved  by  a  linear 
section  between  the  concentrations  of  the  saturated  mixed  crystals. 
Now,  in  this  system,  it  is  not  possible  to  join  the  two  portions  of 
the  conductivity  curve  which  are  interrupted  by  a  linear  portion 
into  a  single  continuous  convex  curve.  Isodimorphism  between  the 
components  might  be  responsible  for  this  condition.  If  such  were 
the  case,  we  should  be  dealing  with  an  additional,  viz.,  a  fourth, 
type,  and  we  would  then  possess  a  means,  i.e.,  by  conductivity 
measurements,  of  distinguishing  between  the  cases  of  isomorphism 
and  isodimorphism.  However,  there  is  not  sufficient  experimental 
material  available  to  warrant  such  general  conclusions:  in  par- 
ticular, the  gap  in  miscibility  may  be  much  wider  than  assumed  by 
Guertler.1 

Decrease  in  specific  conductivity  appears  to  constitute  a  most 
sensitive  test  of  miscibility  in  the  crystalline  state.2  In  many 
cases,  e.g.,  in  the  system  Cu-Co,  which  has  been  mentioned,  this 
method  will  be  found  suited  to  accurate  determination  of  the  extent 
of  the  gap  in  miscibility  of  the  components.  In  other  cases,  e.g., 
in  the  systems  Au-Cu  and  Cu-Ag  (see  above),  it  appears  much 
inferior  to  the  thermal  and  microscopic  methods  in  this  respect. 

When,  in  case  of  complete  isomorphism  between  the  two  com- 
ponents, a  melt  solidifies  after  the  manner  of  a  pure  compound,  we 
are  not  at  liberty  to  conclude,  aside  from  all  other  considerations, 
that  a  compound  is  existent  (p.  193).  Guertler  assumes  that  if  a 
compound  exists,  the  conductivity-concentration  curve  will  be 
composed  of  two  branches,  as  shown  in  Fig.  94b,  and  must,  there- 

1  OSMOND,  Bull.  soc.  encouragement  (V)  2,  1,  837  (1897). 

2  Recently  published  results  by  STOFFEL  (Z.  anorg.  Chem.,  53,  137  (1907)) 
appear  in  a  light  contradictory  to  the  above  statement.      According  to 
Stoffel,  tin  forms  mixed  crystals  with  lead,  and  also  with  cadmium,  to  a  limited 
extent.     Since  an  approximately  linear  relation  between  conductivity  and 
volume-concentration  has  been  determined  in  these  cases  (see  p.  243),  further 
test  of  the  former  results  is  to  be  desired.     Compare  also  SACKUK,  Z.  Elek- 
trochemie,  10,  522  (1904). 


TWO  COMPONENT  SYSTEMS.  249 

fore,  show  a  sharp  peak  at  the  concentration  of  the  compound.  A 
priori,  this  assumption  does  not,  of  necessity,  need  to  hold  true, 
even  if  absolute  accuracy  be  conceded  to  the  purely  empirical  rules 
relating  to  conductivity,  since  we  know  nothing  concerning  the 
degree  of  dissociation  of  a  crystallized  compound  which  forms 
mixed  crystals  with  its  components.  Thus,  the  absence  of  such  a 
peak  fails  to  justify  a  negative  conclusion  regarding  the  possibility 
of  existence  of  a  compound,  even  in  case  of  isomorphous  mixtures. 
3.  DETERMINATION  OF  THE  TEMPERATURE  COEFFICIENT  OF 
ELECTRICAL  CONDUCTIVITY.  —  According  to  CLAUSIUS,  the  specific 
conductivity  of  metals  is  approximately  proportional  to  the 
absolute  temperature.  Denoting  the  specific  resistivity  of  a  metal 
at  0°  C.  by  A0,  and  at  t°  C.  by  At,  according  to  the  above, 
At  =  A0  (I  +  at), 

where  a  is  the  same  for  all  metals,  and  is  equal  to  the  expansion 
coefficient  of  a  gas.  The  value  a  =  0.004  is  sufficiently  close  in 
this  connection,  on  account  of  the  solely  approximate  validity  of  the 
law.  Polymorphous  transformations,  so  far  as  they  are  attended 
by  appreciable  alteration  in  the  electrical  behavior  of  the  material, 
are  excluded  from  the  following  discussion. 

We  are  primarily  indebted  to  MATTHIESSEN  and  VoGT1  for 
experimental  material  relating  to  the  temperature  coefficient  of 
electrical  conductivity.  The  following  regularity  discovered  by 
them  is  of  value  for  our  present  purpose.  We  will  indicate  the 
measured  specific  resistivity  of  an  alloy  by  C.  If  the  specific  con- 
ductivity should  show  a  linear  relationship  to  the  volume-concen- 
tration (see  p.  243),  we  might  calculate  the  former,  according  to 
the  rule  of  mixture,  from  the  conductivities  of  the  components. 
We  will  indicate  the  specific  resistivity,  calculated  in  this  manner, 
by  A.  Now,  Matthiessen  and  Vogt  found  the  following  rule  to  hold 
well  in  many  cases: 

"The  difference  between  measured  and  calculated  resistivity  is 
independent  of  the  temperature." 

That  is,  C  —  A  =  constant  for  each  single  mixture. 

LiEBENOW2  brought  forward  the  following  equation  (called  by 

1  MATTHIESSEN  and  VOGT,  Fogg.  Ann.,  122,  19  (1864). 

2  LIEBENOW,  Z.  Elektrochemie,  4,  201,  217    (1897).      Compare  also  the 
account  of  "  Liebenow's  Theory  and  Its  Consequences,"  by  NERNST,  Theoret. 


250  THE   ELEMENTS   OF   METALLOGRAPHY. 

him  the  leading  equation)  for  the  relation  between  specific  resistiv- 
ity and  temperature  of  alloys: 

C0  (1  +  rt)  =  A0  (1  +  at)  +  50  (1  +  fit).  (1) 

In  this  equation,  C0  and  A0  signify  measured  and  calculated  con- 
ductivities, respectively,  at  0°  C.,  t  signifies  the  temperature  in 
degrees  centigrade,  f,  the  actually  observed  temperature  coefficient 
of  specific  resistivity,  a,  the  temperature  coefficient  of  the  pure 
metals,  B0,  the  "addition  resistivity"  which  results  from  alloying 
the  two  metals  at  0°,  and  /?,  the  temperature  coefficient  of  the 
latter. 

Thus,  Liebenow  divides  the  total  resistivity  of  an  alloy  into  two 
parts,  A  and  B,  of  which  A  is  attributed  to  the  metals  in  a  purely 
individual  connection,  while  B  is  due  to  simultaneous  presence  of 
the  two  metals.  It  is  obviously  of  no  consequence,  as  regards  the 
deductions  which  we  shall  draw  from  the  above  equation,  whether 
the  "  addition  resistivity"  be  ascribed  to  presence  of  thermo- 
electric forces,  pursuant  to  Liebenow's  procedure,  or  be  regarded 
as  incidental  to  the  structure  of  the  alloy  (appearance  of  mixed 
crystals,  etc.).  Liebenow  accounts  for  the  regularity  discovered 
by  Matthiessen  and  Vogt  by  placing 


in  closest  approximation,  for  these  cases.     He  then  obtains 

C0  (1  +  rt)  =  A0  (1  +  at)  +  B0.  (2) 

As  long  as  this  equation  holds,  any  term  including  t  has  the  same 
value  as  when  Z-free.  Thus,  we  obtain 

C0  =  A0  +  B0  (3) 

and 

Cor  =  AQa,  or^  =  -.  (4) 

^o     r 

Equation  4  corresponds  to  a  rule  also  given  by  Matthiessen  and 
Vogt,  from  which  they  derived  the  first  by  transformation. 

We  may  draw  the  following  (Liebenow's)  conclusions  from  the 
above  equations: 

(a)  If  B0  =  0,  then  C0  =  A0  and  7-  =  a.  The  measured  resis- 
tivity is  equal  to  the  calculated  resistivity  at  all  temperatures,  and 


TWO  COMPONENT  SYSTEMS.  251 

its  temperature  coefficient  is  equal  to  that  of  the  resistivity  of  the 
pure  metals.  We  have  become  familiar  with  five  metal  pairs  which 
behave  approximately  in  this  manner  (p.  243). 

(b)  If  B0  is  large  in  comparison  with  A0,  then,  —  =  — - — 
(large).  A°          A°  ? 

Alloys  of  highly  reduced  specific  conductivity  thus  possess  a 
small  temperature  coefficient  of  conductivity. 

The  curve  which  represents  the  temperature  coefficient  of 
specific  resistivity,  and,  likewise,  the  temperature  coefficient  of 
specific  conductivity,  at  a  given  temperature  in  its  relation  to  con- 
centration, must,  according  to  the  above,  show  a  course  analogous 
to  that  of  the  curve  which  represents  the  specific  conductivity 
itself  in  its  relation  to  concentration. 

Thus,  on  entering  in  a  coordinate  system,  the  values  for  tem- 
perature coefficient  of  specific  conductivity  at  a  given  tempera- 
ture in  their  relation  to  concentration,  we  obtain  a  straight  line  for 
case  (a),  i.e.,  a  diagram  analogous  to  the  conductivity-concen- 
tration diagram  corresponding  to  this  case  (Fig.  94a)  with  the  mere 
reservation  that  this  line  must  run  in  a  nearly  horizontal  direction 
on  account  of  the  approximate  equality  between  the  temperature 
coefficients  of  conductivity  for  both  metals.  In  all  other  cases  as 
well,  the  character  of  the  curve  remains  the  same,  in  that  its  form 
preserves  an  analogy  to  that  of  the  corresponding  conductivity- 
concentration  curve  (Fig.  94b,  94c,  or  a  more  complicated  curve 
obtained  by  various  combinations  —  compare  p.  246 — between 
a,  b  and  c,  Fig.  94). 

The  above  deductions  from  equation  (2)  —  under  a  and  b  — 
led  GuERTLER1  to  propose  determination  of  the  temperature  coeffi- 
cient at  different  concentrations  as  a  means  of  establishing  the 
constitution  of  metallic  alloys.  He  would  obviate,  in  this  way,  the 
difficult  task  of  directly  determining  conductivity  in  brittle  alloys. 
The  "addition  resistivity"  B  is  attributed  to  mixed  crystal  for- 
mation, according  to  LeChatelier.  Guertler  also  assigns  a  specific 
"compound  resistivity"  to  chemical  compounds. 

Relative  to  the  reliability  of  this  method,  it  may  be  noted  that 
both  of  Matthiessen  and  Vogt's  rules,  and  the  equivalent  equation 

1  GUERTLER,  Z.  anorg.  Chem.,  54,  58  (1907).  Compare  also  LIEBENOW, 
Z.  Elektrochemie,  4,  219,  (1897). 


252  THE  ELEMENTS   OF  METALLOGRAPHY. 

2,  possess  none  other  than  conditional  validity.  For  example, 
although  it  follows  from  equation  4  that  7-  is  always  positive,  since 
C0,  AQ  and  a  are  always  positive,  there  are  alloys  which  possess 
negative  temperature  coefficients  of  resistivity  below  certain  tem- 
peratures, e.g.,  Cu-Ni  and  Cu-Mn  alloys.1  If  the  above  division  of 
total  resistivity  into  two  parts  is  to  be  retained  in  such  cases,  only 
the  general  equation  (1),  in  which  /?  assumes  a  negative  value 
throughout  the  respective  temperature  range,  remains  valid,  accord- 
ing to  Liebenow. 

In  consideration  of  the  conditional  accuracy  of  Matthiessen  and 
Vogt's  rules,  of  errors  which  may  be  introduced  owing  to  occur- 
rence of  polymorphic  transformation  and  of  the  scarcity  of  experi- 
mental material,  we  are  not  inclined  to  attach  great  importance  to 
determination  of  the  temperature  coefficient  of  conductivity  as  an 
independent  method  of  establishing  the  constitution  of  alloys  in 
general.  Obviously,  it  is  capable  of  supplying  evidence  of  a  con- 
firmatory nature  in  certain  cases.  An  example  of  this  is  to  be  found 
in  Liebenow's  location  of  the  compound  Cu-Zn  by  the  aid  of  this 
method.2  In  many  cases,  determination  of  the  relation  between 
conductivity  and  temperature  may  be  advantageously  applied 
in  the  demonstration  of  polymorphous  transformation.3 

4.  DETERMINATION  OF  THE  VAPOR  PRESSURE  OF  A  COMPONENT. 
—  A  salt  containing  water  of  crystallization  may  hold  its  several 
water  molecules  with  varying  tenacity.  By  way  of  example,  we 
may  cite  blue  vitriol,  CuS04  +  5  H2O,  which  slowly  effloresces  at 
ordinary  temperature,  gives  off  four  molecules  of  water  in  the 
drying  oven  at  100  degrees,  and  loses  its  last  molecule  of  water 
at  temperatures  above  200  degrees.  Thus,  such  a  salt  forms  a 
number  of  compounds  with  water,  called  hydrates.  An  accurate 
insight  into  the  conditions  which  prevail  here  is  to  be  obtained 
by  determining  the  aqueous  tensions  at  constant  temperature  of 
samples  of  salt  which  contain  varying  amounts  of  water. 

We  will  first  consider  a  rather  simple  case  in  which  the  respective 
salt  forms  no  hydrate  under  the  chosen  experimental  conditions. 

1  FEUSSNER  and  LINDECK,  Abh.   d.  Phys.-Techn.   Reichsanstalt,  2,   501 
(1895). 

2  LIEBENOW,  Z.  Elektrochemie,  4,  234  (1897). 

8  LECHATELIER,  Revue  g&ierale  des  sciences,  6,  533  (1895):  Contribu- 
tion a  l'e"tude  des  alliages,  p.  448. 


. 
|  -  PC 


TWO  COMPONENT  SYSTEMS.  253 

1 

Ordinary  salt  —  sodium  chloride  —  is  well  suited  to  this  purpose, 
and  our  task  is,  in  effect,  to  study  the  aqueous  tension  in  the 
system,  NaCl-H2O,  at  all  possible  concentrations;  but  with  re- 
striction as  to  temperature,  which  we  will  recognize  by  choosing 
the  temperature  50°  C.  We  will  effect  the  determination  in  the 
following  manner:  An  aqueous  solution  of  sodium 
chloride  of  definite  concentration  is  enclosed  in  an 
evacuated  cylinder  A  (Fig.  96),  fitted  with  an  air- 
tight piston  B.  Since  sodium  chloride  does  not 
evaporate  to  a  measurable  extent,  water  vapor 
alone  can  be  present  in  the  closed  space  above  the 
solution.  We  will  assume  that  determination  of  the 
pressure  of  the  water  vapor,  which  serves  as  a 
measure  of  its  concentration  in  the  gas  chamber,  may 
be  effected  at  any  time  by  means  of  the  mano- 
meter  C. 

According  to  the  law  of  vapor-pressure  lowering,  pIQ  Q6 
which  is  quite  analogous  to  the  law  of  melting- 
point  lowering,  the  vapor  pressure  of  pure  water  will  be  lowered 
by  solution  of  another  substance  to  an  extent  which  is  propor- 
tional to  the  concentration  of  the  solution.  The  vapor  pressure 
over  a  solution  is  unequivocally  fixed  at  any  given  temperature, 
since  the  pressure  over  the  solution  is  unequivocally  fixed  at  any 
given  temperature.  Since  the  pressure  of  vapor  over  pure  water 
at  50  degrees  is  about  92  mm.  of  mercury,  the  pressure  of  vapor 
over  the  solution  will  be  less  than  92  mm.  We  will  assume  that  it 
approximates  91  mm.  Now,  on  gradually  raising  the  piston  in 
our  cylinder,  further  vaporization  of  water  from  the  sodium  chlo- 
ride solution  results.  On  this  account,  the  solution  becomes  more 
concentrated,  and  a  lowering  of  the  vapor  tension  takes  place. 
This  lowering  will  continue  until  the  solution  becomes  saturated 
with  sodium  chloride.  The  vapor  tension  of  a  saturated  solu- 
tion of  sodium  chloride  at  50  degrees  amounts  to  approximately 
70  mm.  If,  now,  further  increase  in  the  volume  of  the  gas 
chamber  and  further  evaporation  of  water  are  effected  by  con- 
tinual elevation  of  the  piston,  no  change  in  vapor  pressure  can 
result,  since  the  saturated  solution  can  suffer  no  change  in  con- 
centration at  constant  temperature.  By  further  evaporation  of 
water,  merely  the  amount  of  saturated  solution  changes,  in  that 


254  THE   ELEMENTS   OF  METALLOGRAPHY. 

a  definite  amount  of  sodium  chloride  crystallizes  out  for  every 
gram  of  water  which  leaves  the  solution.  The  vapor  tension  of  the 
solution,  i.e.,  the  concentration  of  water  vapor  in  the  gas  chamber, 
is,  nevertheless,  independent  of  the  amount  of  solution  present. 
Thus,  from  the  moment  when  the  first  crystal  of  sodium  chloride 
separates,  we  have  equilibrium  between  the  three  phases  of 
invariable  composition:  "saturated  solution,  crystallized  sodium 
chloride  and  water  vapor  at  70  mm.  pressure."  The  equation  of 
the  reaction  may  be  written  in  the  form: 

(NaCl  +  nH2O)  ±;  NaCl  +  nH20,     (t  =  50°). 

Satd.  Soln.  Cryst.          Water  vapor 

at  70  mm.  pressure. 

Elevation  of  the  piston  causes  reaction  to  take  place  from  left 
to  right;  it  effects  a  decrease  in  the  amount  of  saturated  solution 
and  an  increase  in  the  amount  of  sodium  chloride  crystals  and 
water  vapor  —  no  one  of  the  phases  changes  its  composition 
until  the  last  drop  of  saturated  solution  has  disappeared.  De- 
pression of  the  piston  causes  reaction  to  proceed  in  the  opposite 
direction,  whereby  the  pressure  of  the  water  vapor  remains  con- 
stant as  long  as  the  last  salt  crystal  remains  undissolved.  On 
account  of  the  invariability  of  composition  of  each  phase  which 
takes  part  in  the  equilibrium,  the  term,  complete1  (heterogeneous) 
equilibrium  is  used  in  this  connection. 

When,  on  continued  elevation  of  the  piston,  the  last  trace  of 
water  has  passed  from  the  liquid  phase  into  the  gas  chamber, 
there  is  a  momentary  condition  of  equilibrium  between  crystal- 
lized salt  and  water  vapor  at  70  mm.  pressure.  Further  eleva- 
tion of  the  piston  can  simply  result  in  an  increase  in  the  volume 
of  water  vapor,  and  a  corresponding  decrease  in  vapor  pres- 

1  The  complete  equilibrium  which  here  obtains  is  perfectly  analogous  to 
that  hitherto  considered.  Up  to  the  present,  we  have  regarded  -the  pressure 
exerted  upon  the  system  as  unchangeable  (=1  atm.);  the  temperature,  how- 
ever, subject  to  alteration.  Equilibrium  was  complete  as  long  as  change  in 
the  heat  content  of  the  system  was  unaccompanied  by  change  in  tempera- 
tufe  (see  p.  33,  and,  concerning  the  idealization  generally  underlying  this 
interpretation,  pp.  281  and  282).  In  the  present  instance,  we  maintain  the 
temperature  of  the  system  constant,  and  equilibrium  is  complete  as  long  as 
a  change  of  volume  is  unaccompanied  by  a  change  of  pressure.  In  both  cases, 
the  composition  of  every  phase  remains  unchanged  during  progress  of  the 
reaction  in  either  direction,  until  one  of  the  phases  is  exhausted. 


TWO  COMPONENT  SYSTEMS. 


255 


sure,  which  may  be  calculated  with  ease  under  the  assumption 
that  the  gas  laws  hold  in  this  case.  It  is  clear  that,  by  using  a 
cylinder  of  sufficient  length,  we  may  cause  the  pressure  of  water 
vapor  above  the  salt  crystals  to  fail  below  any  chosen  value,  i.e., 
to  finally  approximate  zero. 

We  may  combine  our  experimental  results  in  a  volume-pressure 
diagram,  as  shown  in  Fig.  97a.     The  volume  of  the  gaseous  phase, 

Aqueous  Tension  in  mm.  Mercury 


Water  Vapor +  Unsat'd  SoVn 


-    Water  Vapor  +  Safd  SoVn+  Crystals 


Water  Vapor  +  Crystals 


FIG.  97a. 

measured  by  the  length  to  which  the  piston  has  been  drawn  out, 
is  entered  upon  the  horizontal  axis,  and  the  corresponding  pressure 
of  the  water  vapor  in  the  gas  chamber,  shown  by  our  manometer, 
is  entered  upon  the  vertical  axis.  We  see  that  the  volume-pressure 
curve  consists  of  three  distinct  branches  which  correspond  to  the 
three  different  conditions  of  the  system.  In  the  case  of  a  suf- 


256  THE  ELEMENTS   OF   METALLOGRAPHY. 

ficiently  dilute  solution,  a  (the  highest  point  on  the  branch  ab) 
practically  coincides  with  a  point  representing  the  vapor  tension 
of  pure  water  at  this  temperature.  Between  a  and  b  we  have  a 
system  composed  of  two  phases  —  vapor  and  solution  of  salt  in 
water;  the  latter  increasing  in  concentration  as  the  pressure  falls. 
The  solution  has  reached  its  maximum  concentration  at  the  point 
6,  and,  beginning  with  this  point,  we  note  the  added  presence  of 
crystallized  sodium  chloride  in  the  system.  Thus,  the  horizontal 
portion  be  corresponds  to  a  system  composed  of  three  phases, 
namely,  water  vapor,  saturated  salt  solution  and  crystallized  salt. 
At  the  point  c,  all  of  the  water  has  vaporized,  so  that  the  system 
again  consists  of  two  phases,  in  this  case,  of  water  vapor  and 
crystallized  salt.  We  see  that  the  vapor  pressure  above  crys- 
tallized salt  is  undefined,  in  that  it  may  assume  any  value  between 
zero  and  that  corresponding  to  the  saturated  solution  at  c  (the 
point  d  represents  intersection  of  the  branch  cd  with  the  volume 
axis  at  V  =  <*>).  This  signifies  purely  that  sodium  chloride 
crystals  may  be  kept  at  50  degrees  without  change,  in  a  space 
containing  water  vapor,  provided  the  pressure  of  the  water 
vapor  is  less  than  the  vapor  tension  of  the  saturated  sodium 
chloride  solution  at  this  temperature.  If  the  pressure  of  the 
water  vapor  is  exactly  equal  to  that  of  the  saturated  solution,  the 
relative  amounts  of  crystallized  sodium  chloride  and  saturated 
solution  present  will  depend  upon  the  amount  of  space  available 
for  the  vapor  phase.  These  relative  amounts  remain  unchanged 
at  constant  volume. 

A  concentration-pressure  diagram  (Fig.  97b)  is  better  adapted 
to  our  purposes  than  the  volume-pressure  diagram  just  dis- 
cussed. The  average  concentration  of  the  existent  liquid  and  crys- 
talline phases  (in  either  molecular  or  weight  per  cent)  is  entered 
along  the  concentration  axis,  and  the  pressure  of  water  vapor  in 
equilibrium  with  the  other  phases  at  this  temperature  (50  degrees) 
is  entered  along  the  pressure  axis.  Here,  as  in  the  previous  case, 
the  portion  ab  corresponds  to  equilibrium  between  solution  (pure 
NaCl  +  H2O)  and  vapor,  and  the  horizontal  portion  be  corre- 
sponds to  equilibrium  between  solution  (pure  NaCl  +  H20), 
crystallized  sodium  chloride  (pure)  and  vapor.  The  portion  cd 
here  coincides  with  the  pressure  axis,  in  accordance  with  the 
capability  of  vapor  at  different  pressures  to  remain  in  equilibrium 


TWO  COMPONENT  SYSTEMS.  257 

with  pure  sodium  chloride.  Conversely,  if  a  system  shows  the 
relations  represented  in  the  two  preceding  figures,  we  are  at 
liberty  to  draw  the  conclusion  that  we  are  dealing  with  a  pure  salt, 
i.e.,  that  the  salt  forms  no  compound,  or  hydrate,  with  water. 

HZO  Nad 


80 


Molecular  per  cent  NaCl  in  the  Liquid  and  Crystalline  Phase.         100 
FIG.  97b. 

We  will  now  proceed  to  consider  the  vapor-tension  values  for  all 
possible  concentrations  in  the  system  copper  sulphate-water  at 
constant  temperature.  Fig.  98a  gives  the  approximate  course  of 
the  volume-pressure  curve  for  this  system.  On  continually  in- 
creasing the  volume  of  the  gas  phase,  we  obtain  here,  as  in  the 
case  previously  considered,  an  increasing  depression  of  vapor  pres- 
sure corresponding  to  the  branch  ab  of  the  curve  (Fig.  98a),  until 
the  saturation  concentration  of  the  solution  is  reached,  and  crys- 
tallization of  blue  vitriol  (CuSO4  +  5  H2O)  first  sets  in.  The 


^L 


*       A 


G     d 


80 
O» 


SOOOOOO 
O  TJ4  CO  W  T-t 

•iuw  ui  uoisudj,  snodriby 


TWO  COMPONENT  SYSTEMS.  259 

pressure  of  water  vapor  above  the  saturated  solution  amounts  to 
87  mm.  at  this  point,  and,  corresponding  to  the  horizontal  portion 
be,  remains  constant,  in  spite  of  continued  elevation  of  the  piston, 
until  the  last  drop  of  solution  has  disappeared.  All  of  the  copper 
sulphate  is  now  in  the  form  of  solid  hydrate,  CuSO4  +  5  H2O.  On 
further  enlarging  the  gas  chamber,  a  lowering  of  vapor  pressure 
along  the  curve  cd  is  at  first  noted.  However,  this  lowering  will 
continue  only  as  long  as  the  hydrate,  CuSO4  +  5  H2O,  remains 
unchanged.  Such  a  condition  is  realized  at  pressures  above  47  mm. 
When  this  pressure  is  reached,  it  is  noted  that  the  manometer 
indicates  no  change  in  pressure  as  the  piston  is  further  raised. 
This  is  represented  by  the  horizontal  branch  de,  and  is  due  to  the 
fact  that  blue  vitriol  (CuSO4  +  5  H2O)  now  loses  water,  either 
partially  or  completely  (the  subsequent  description  supplies  posi- 
tive information  in  this  respect).  Assuming  that  the  former  is 
true,  in  that  two  molecules  of  water  are  lost  at  this  point,  we 
may  write  the  equation: 

(CuSO4  +  5  H2O)  <=»  (CuSO4  +  3  H2O)  +  2  H2O,     (t  =  50°), 

Cryst.  Cryst.  Water  vapor  at 

47  mm.  pressure. 

to  cover  this  new  condition  of  complete  equilibrium.  Elevation 
of  the  piston  causes  reaction  to  take  place  from  left  to  right;  it 
effects  a  decrease  in  the  amount  of  water-rich  hydrate,  and  an 
increase  in  the  amount  of  lower  hydrate  and  water  vapor,  without 
changing  the  composition  of  any  phase;  for,  as  long  as  a  crystal  of 
water-rich  hydrate  remains,  the  vapor  pressure  cannot  fall  below 
the  value  at  which  this  hydrate  loses  water.  When  the  last 
crystal  of  water-rich  hydrate  has  disappeared,  however,  further 
elevation  of  the  piston  causes  dilution  of  the  water  vapor,  and. 
therefore,  lowering  of  its  pressure  (along  ef),  until  the  hydrate, 
CuSO4  +  3  H2O,  begins  to  lose  water.  This  decomposition  occurs 
at  30  mm.,  and  a  third  period  of  constant  vapor  pressure  ensues, 
according  to  the  equation: 

(CuS04  +  3  H2O)  <=i  (CuSO4  +  1  H2O)  +  2  H2O,     (t  =  50°). 

Cryst.  Cryst.  Water  vapor 

at  30  mm.  pressure. 

The  above  period  continues  until  the  last  crystal  of  hydrate, 
CuS04  +  3  H2O,  has  become  transformed  into  the  lowest  hydrate, 
CuSO4  +  1  H2O.  Not  until  then,  can  further  increase  in  volume 


260 


THE  ELEMENTS   OF  METALLOGRAPHY. 


cause  renewed  lowering  of  vapor  pressure.  The  course  of  this 
fourth  lowering  is  indicated  by  the  curve  gh.  Thus,  it  continues 
until  a  pressure  of  4.4  mm.  is  reached,  when  the  last  molecule  of 
water  is  lost,  and  a  fourth  period  of  constant  pressure  is  shown  by 
the  manometer.  This  is  indicated  by  the  horizontal  hi,  and  ceases 
when  the  very  last  trace  of  water  has  entered  the  gas  phase.  The 
equation  of  the  reaction  is  as  follows: 

[CuSO4  +  1  H2O]  <=±  CuSO4  + 1  H20,         (t  =  50°). 


Cryst. 


Cryst. 


Water  vapor  at 
4.4  mm.  pressure. 


Continuous   decrease   of   vapor   pressure  toward   the    zero   limit 
accompanies  further  (continuous)  increase  in  volume.      This  is 


1UU 

a 

90 

\b 

C 

80 

§  T0 

r 

, 

•§50 

-  | 

d     $ 

§ 

1  40 

73 
"1 

| 

r1 
C 

>        /                      0 

I30 

u 

i 

2     6 

^20 

f 

h" 

10 

V 

1                      A 

0 

, 

,    i    ,                         .         ,        .        .      k 

CuSoi-H2O  100 

Molecular  per  cent  Copper  Sulphate  in  the  Liquid 
and  Crystalline  Phases 

FIG.  98b. 


indicated  by  the  branch  ik  which  approaches  the  volume  axis 
asymptotically. 

Fig.  98b  shows  the  arrangement  of  these  results  in  a  concen- 
tration-pressure diagram.  As  in  the  analogous  diagram,  Fig.  97b, 
the  average  concentration  of  existent  liquid  and  crystalline  phase, 


TWO  COMPONENT  SYSTEMS.  261 

expressed  in  molecular  per  cent,  is  entered  along  the  axis  of 
abscissas.  Corresponding  breaks  in  both  curves,  98a  and  b,  are 
lettered  in  the  same  manner.  We  again  recognize  the  fact 
observed  relative  to  the  system  NaCl-H2O  that  a  single  crystal- 
line variety  may  be  in  equilibrium  with  water  vapor  at  varying 
pressures. 

Thus,  the  hydrate,  CuSO4  +  5  H2O,  is  in  equilibrium  (at  50 
degrees)  with  water  vapor  of  any  pressure  between  d  and  c, 
i.e.,  it  may  remain  infinitely  long  in  contact  with  water  vapor 
at  any  of  these  pressures,  without  efflorescence  or  deliquescence. 
If  a  vapor  pressure  c  exists  in  the  gas  chamber,  it  then  depends 
upon  the  relation  of  the  size  of  the  latter  to  the  quantity  of 
water  present  in  the  system  whether  the  copper  sulphate  will  occur 
as  saturated  solution,  as  crystallized  hydrate,  CuSO4  +  5  H2O, 
or  as  a  mixture  of  both.  If  a  vapor  pressure  d  exists  in  the 
gas  chamber,  the  same  is  true  with  respect  to  the  two  phases, 
CuSO4  +  5  H2O  and  CuSO4  +  3  H2O.  Thus,  the  vapor  pressure 
is  definitely  fixed  for  any  given  concentration  value  only  when  an 
amount  (even  though  trifling)  of  the  second  phase  (saturated 
solution  or  another  hydrate)  is  present.  Consequently,  it  is 
incorrect,  at  least  in  principle,  to  speak  of  an  aqueous  tension  of 
the  hydrate,  CuSO4  +  5  H2O,  for  example,  without  adducing  further 
information  as  to  whether  this  is  the  tension  at  which  the  crystals 
may  absorb  water  (deliquesce)  or  that  at  which  they  may  lose 
water  (effloresce).  We  shall,  nevertheless,  simply  designate  the 
aqueous  tension  of  a  hydrate  as  that  tension  at  which  it  may  lose 
water,  i.e.,  that  which  corresponds  to  equilibrium  with  the  lower 
hydrate.  In  this  sense,  the  tension  of  the  horizontal  be  is  that  of 
the  saturated  solution;  de,  that  of  the  hydrate,  CuSO4  +  5  H2O; 
fg,  that  of  the  hydrate,  CuSO4  +  3  H2O;  and  hi,  that  of  the  hydrate, 
CuSO4  +  1  H2O. 

We  accordingly  perceive  that  there  are  as  many  different 
hydrates,  if  the  saturated  solution  be  included  in  the  total,  as 
horizontal  portions  in  our  step-formed  vapor-pressure  curve,  and  it 
follows  that,  in  the  determination  of  the  relation  between  vapor 
pressure  and  concentration,  we  possess  a  means  of  ascertaining  the 
number  of  compounds  which  a  given  salt  forms  with  water. 

Possible  complications  will  not  be  considered.  The  experi- 
mental determination  may  be  carried  out  by  simply  placing  hy- 


262  THE  ELEMENTS   OF   METALLOGRAPHY. 

drates  which  have  been.deprived  of  successively  increasing  amounts 
of  water  in  the  vacuum  of  a  barometer  tube  and  measuring  the  de- 
crease in  height  of  the  mercury  column  after  pressure  has  reached 
self-adjustment.  The  determination  may  be  made  in  many  other 
ways,  however.1 

An  investigation  by  ANDREA2  has  served  to  dispel  any  possible 
doubt  relative  to  the  occurrence  of  discontinuous  change  in  vapor 
tension,  as  above.  Such  change  is  wedded  to  the  condition  that 
one  phase  disappear  completely  at  a  given  temperature,  and  that 
another  take  its  place,  as  may  be  seen  at  once  from  the  diagram 
(Fig.  98b).  Thus,  in  concentrations  to  the  left  of  cd,  the  saturated 
solution  is  stable  in  the  presence  of  hydrate,  CuSO4  +  5  H2O,  and  in 
those  to  the  right  of  this  line  the  hydrate,  CuSO4  +  3  H2O,  is  stable 
in  the  presence  of  penta-hydrate.  Consequently,  a  condition  of 
practical  immiscibility  must  characterize  the  mutual  relations  of 
the  phases.  If  such  is  not  the  case,  we  are  confronted  by  relations 
such  as  those  occurring  between  a  and  6,  according  to  which  the 
composition  of  the  liquid  phase  and  the  vapor  pressure  vary  con- 
tinuously from  pure  water  a  to  saturated  solution  b.  This  class  of 
relationship  between  two  hydrates  will  accordingly  find  expression 
in  the  general  diagram. 

If  our  system  is  composed,  in  a  general  sense,  of  a  volatile  and 
a  practically  non-volatile  substance,  in  place  of  water  and  a  salt, 
we  may  obviously  make  use  of  the  practical  information  outlined 
above  in  determining  whether  chemical  combination  occurs  be- 
tween these  components  or  not.  Any  appearance  of  the  non-vola- 
tile component  in  the  gas  phase  (either  in  the  pure  state  or  as  a 
compound)  is  precluded,  however,  if  the  method  is  to  be  adjudged 
reliable.  The  relations  in  other  systems  may  be  much  more  com- 
plicated. This  method  has  been  of  little  service  in  metallo- 
graphical  investigation,  since  the  vapor  pressure  of  most  metals  is 
extremely  small,  except  at  such  high  temperatures  that  very  con- 
siderable experimental  difficulty  is  connected  with  its  determina- 
tion. The  above  detailed  description  of  this  method  has  been 
introduced  chiefly  in  consideration  of  the  method  to  be  described 
under  6. 

1  Compare,   for   example,   MULLER-ERZBACH,   Z.  phys.    Chem.,    19,   135 
(1896). 

2  ANDREA,  Z.  phys.  Chem.,  7,  241  (1891). 


TWO  COMPONENT  SYSTEMS.  263 

5.  DETERMINATION  OF  THE  SOLUBILITY  OF  A  COMPONENT.  — 
The  comprehensive  analogy  which  characterizes  the  behavior  of 
gases  and  of  solutions  has  been  brought  prominently  into  view 
with   the   development   of   physical    chemistry.     A   particularly 
sharp  expression  may  be  given  to  this  analogy  by  defining  the 
vapor  condition  as  solution  of  a  substance  in  space,  or  in  vacuum. 
If,  in  dealing  with  a  system  composed  of  two  components,  one 
of  which  is  alone  soluble  in  a  third  indifferent  substance  called 
solvent,  we  prepare  a  solubility-concentration  diagram  at  con- 
stant temperature,  relations  of  the  same  general  nature  as  those  * 
characterizing   the   vapor   pressure-concentration   diagram    (dis- 
cussed under  4)  will  be  encountered.     ABEGG  and  HAMBURGER1 
investigated  the  poly  iodides  of  the  alkali  metals  in  this  way, 
using  benzine  as  solvent.     This  method  has  also  found  no  appli- 
cation in  the  study  of  metallic  alloys. 

6.  DETERMINATION  OF  ELECTROLYTIC  SOLUTION  TENSION.  — 
Chemical  change  is  invariably  associated  with  the  solution  of  a 
metal  in  any  other  substance  which  is  not  a  metal,  for  example, 
in  water,  so  that  it  is  impossible  to  recover  the  metal  from  its 
solution  by  crystallization.     NERNST  has  shown  that  the  experi- 
ence gained  from  investigation  of  ordinary  solution  processes,  e.g., 
the  solution  of  sugar  in  water,   may,  nevertheless,  be  used  to 
explain  the  process  of  solution  of  metals  in  water,  by  ascribing  a 
so-called  electrolytic  solution  tension  to  the  metal  in  place  of  the 
ordinary  solution  tension  associated  with  other  substances.     The 
electrolytic  solution  tension  of  a  metal  represents  the  tendency 
of  the  latter  to  pass  into  solution,  not  as  molecules,  but  as  positive 
ions,  and  plays  fundamentally  the  same  role  as  vapor  tension  and 
ordinary  solution  tension  (discussed  under  4  and  5,  respectively). 
Thus,  if  we  have  a  system  of  two  metals,  one  of  them  possessing  a 
strong  tendency  to  pass  into  the  ionic  condition,  and  the  other 
possessing  practically  no  such  tendency,  we  are  in  a  position  to 
obtain  complete  information  regarding  the  mutual  relations  of 
the  two  metals  at  the  corresponding  temperature  by  working  out 
an   " electrolytic  solution  tension-concentration  diagram."     The 
metal  of  considerable  solution  tension  is  called  a  base  metal, 
while  that  of  inappreciable   solution  tension  is   called   a  noble 
metal.     Viewing  Fig.  97b  in  the  above  light,  i.e.,  as  electrolytic 

1  ABEGG  and  HAMBURGER,  Z.  anorg.  Chem.,  50,  403  (1906). 


264  THE  ELEMENTS   OF   METALLOGRAPHY. 

solution  tension-concentration  diagram,  in  which  the  concentra- 
tion axis  is  graduated  in  atomic  per  cents  of  the  noble  metal  B, 
we  must  recognize  solubility  of  the  two  metals  within  the  con- 
centration range  a-b.  Within  the  concentration  range  b-c,  we 
consider  the  alloy  to  consist  of  a  mixture  of  two  varieties  of 
saturated  mixed  crystals,  one  possessing  the  concentration  a, 
and  the  other  practically  identical  with  the  (pure)  noble  metal. 
Fig.  9Sb,  viewed  in  this  connection,  subscribes,  moreover,  to  the 
existence  of  three  compounds  between  these  metals,  of  the  respec- 
tive formulas,  A5B,  A3B  and  AB. 

The  solution  tension  value  defines,  within  range  of  an  additive 
constant,1  the  potential  difference  between  the  alloy  in  a  solution 
of  the  base  metal  of  definite  ionic  concentration,  and  any  normal 
electrode.  Thus,  a  continuous  or  an  abrupt  change  in  solution 
tension  corresponds  to  a  continuous  or  an  abrupt  change  in  such 
potential  difference,  and  the  prosecution  of  this  method  lies,  for 
the  most  part,  in  the  direction  of  potential  measurement.  Accord- 
ing to  SACKUR,2  the  relation  between  the  solution  tension  of  a 
pure  metal  A  and  that  of  an  alloy  of  this  metal  with  a  second 
metal  B  may  be  established  by  experimental  determination  of 
the  equilibrium  concentrations  up  to  which  the  metal  A}  on  the 
one  hand  in  pure  condition  and  on  the  other  hand  alloyed  with 
B,  is  capable  of  displacing  the  metal  B  from  its  salt  solution. 

The  method  of  determination  of  electromotive  force  for  investi- 
gating the  constitution  of  alloys  was  first  applied  by  LAURIE, 3 
and  later  by  HERSCHKOwrrscn,4  who  was  able  to  eliminate  one  of 
the  possible  sources  of  error5  connected  with   Laurie's  experi- 
ments.    Nevertheless,  it  is  scarcely  possible  to  reconcile  Hersch- 
kowitsch's    results    with    those    obtained    by    thermal    methods. 
On  the  other  hand,  BiJL8   (see  p.  206),  in  an  investigation  of 
cadmium    amalgams,    obtained     complete    agreement    between 
results  based  upon  the  determination  of  electromotive  force  and 
those  furnished  by  the  melting-point  diagram.     Moreover,  he  was 
able,  by  means  of  the  former  method,  to  follow  the  course  of  the 
curve  of  separation,  relative  to  limited  miscibility  of  the  corn- 
Compare,  however,  NERNST,  Z.  phys.  Chem.,  22,  539  (1897). 
SACKUR,  Z.  Elektrochem.,  10,  522  (1904);  Ber.,  38,  2186  (1905). 
LAURIE,  Jour.  Chem.  Soc.,  65,  1031  (1894). 
HERSCHKOWITSCH,  Z.  phys.  Chem.,  27,  123  (1898). 
OSTWALD,  Z.  phys.  Chem.,  16,  750  (1895). 
BIJL,  Z.  phys.  Chem.,  41,  641  (1902). 


TWO  COMPONENT  SYSTEMS.  265 

ponents  in  the  crystalline  condition,  down  to  a  point  correspond- 
ing to  ordinary  temperature.  Absolute  agreement  between  the 
results  of  both  methods  cannot  be  expected,  for,  obviously,  reac- 
tions of  low  velocity,  or  of  very  inconsiderable  heat  tone,  may  be 
overlooked  in  thermal  investigation.  Evidently,  a  parallel 
method  for  determining  the  constitution  of  metallic  alloys,  which 
shall  apply  to  completely  solidified  mixtures  (supplementing  the 
microscopic  method),  is  greatly  to  be  desired  for  purposes  of  com- 
parison, since,  in  the  event  of  general  agreement  between  the 
different  classes  of  results,  our  final  conclusions  would  acquire  a 
greater  degree  of  credibility,  bordering  upon  certainty,  and  then, 
again,  eventual  differences  in  this  connection  would  point  to  the 
occurrence  of  reactions  which  had  escaped  observation  thermally. 
Relative  to  the  value  along  these  lines  of  the  method  now 
under  discussion,  we  may  state  that  it  possesses  an  advantage 
over  the  methods  which  are  based  on  conductivity  determination 
in  that  its  theoretical  foundation  has  been  accurately  estab- 
lished. The  preliminary  condition  that  all  reactions  shall  have 
proceeded  to  completion  is  also  essential  here.  Determinations 
may  be  rendered  more  difficult  by  the  occurrence  of  passivity 
phenomena,  according  to  which  the  metal  in  question  ex- 
hibits a  more  noble  behavior  than  it  should,  in  consequence  of 
conditions  which  are  not  well  understood.  This  defect  could 
invariably  be  overcome,  however,  by  a  suitable  choice  of  electro- 
lyte, or  by  operating  at  an  elevated  temperature.  Care  should 
always  be  taken  that  the  measured  value  of  electromotive  force 
actually  represents  the  end  value.  Bijl  observed  that  in  some 
cases  this  was  true  only  after  several  days  had  elapsed.  The 
circumstance  that  a  relatively  small  change  in  electromotive 
force  corresponds  to  a  considerable  change  in  electrolytic  solu- 
tion tension  (an  increase  of  -  - —  volts  in  the  electromotive 

n 

force  of  an  n-valent  metal  corresponds  to  a  ten-fold  increase  in 
its  solution  tension  at  room  temperature)  cannot,  in  view  of  the 
great  accuracy  which  characterizes  the  experimental  determina- 
tion of  potential  differences,1  be  generally  regarded  as  pre- 
judicial to  the  application  of  this  method, 

1  Compare  in  this  connection,  RICHARDS  and  FORBES,  Z.  phys.  Chem.,  58, 
683  (1907). 


266  THE  ELEMENTS   OF   METALLOGRAPHY. 

7.  DETERMINATION  OF  HEAT  OF  FORMATION.  —  If    chemical 
combination   between   two  substances  is  accompanied  by  con- 
siderable heat  evolution,  different  heat  effects  will  be  observed 
when  the  compound,  on  the  one  hand,  and  the  components   in 
uncombined   condition  in  corresponding  proportions  by  weight, 
on  the  other  hand,  are  dissolved.    This  difference,  neglecting  heat 
of  mixture,  is  equal  to  the  heat  of  combination  of  the  substances. 
Of  course,  we  assume  primarily  that  the  final  nature   of   the 
solution  is  the  same  in  both  cases.     Thus,  the  observation  that 
temperature  elevation  accompanies  solution  of  many  anhydrous 
salts  in  water  frequently  finds  explanation  in  the  formation  of 
hydrates.     This  method  has  not  yet  been  successfully  used  for 
investigating  the  structure  of  metallic  alloys  (concerning  experi- 
mentation, compare  Herschkowitsch,  1.  c.). 

8.  THE  METHOD  OF  ANALYSIS  OF  RESIDUES.  —  When  the  com- 
ponents of  a  compound  offer  varying  resistance  to  the  action  of  a 
certain  chemical  reagent,  the  compound  is  generally  more  resist- 
ant than  the  least  resistant  component.     It  is,  therefore,  possible, 
if  the  alloy  contains  the  less  resistant  component  in  excess,  to 
dissolve  out  the  same,  leaving  pure  compound,  which  latter  may 
then  be  analyzed.     This  process  is  called  the  method  of  analysis 
of  residues.     Much  use  has  been  ma,de  of  it  in  the  past;  fre- 
quently to  good  effect.     Thus,  MYLIUS,  FORSTER  and  ScnoENE1 
isolated  the  iron  carbide  which  is   known   as   cementite,  Fe3C 
(see  p.  228),  in  this  way.     Use  of  the  method  has,  however,  led 
to  erroneous  conclusions  in  numerous  other  cases. 

Determination  of  the  relative  susceptibility  of  alloys  of  various 
concentrations  to  chemical  action  by  acids2  rests  upon  the  same 
basis.  When  two  metals  do  not  unite  chemically,  such  sus- 
ceptibility is  a  continuous  function  of  the  composition  of  the 
alloys,  while,  if  a  compound  occurs,  it  undergoes  discontinuous 
change  at  the  concentration  corresponding  to  the  composition 
of  the  compound. 

Finally,  we  note  that  the  development  of  structure  on  polished 
sections  also  rests  upon  the  same  basis. 

1  MYLIUS,  FORSTER  and    SCHOENE,  Z.  anorg.  Chem.,  13,  38  (1896). 

2  SACKUR,  Z.  Elektrochem.,  10,  526  (1904):  Ber.  38,  2186  (1905). 


CHAPTER  IV. 
THREE   COMPONENT  SYSTEMS. 

GRAPHICAL  representation  of  the  composition  of  a  three  com- 
ponent system  is  best  effected,  according  to  Gibbs,  by  using  an 
equilateral  triangle1  (Fig.  99).  Familiarity  with  the  following 
geometrical  properties  is  essential  in  this  connection. 

(1)  In  an  equilateral  triangle,  the  sum  of  three  lines  drawn 
from  a  point  P  in  the  interior  of  the  triangle  perpendicularly  to 
the  three  sides,  respectively,  is  equal  to  the  altitude  h. 

PD  +  PE  +  PF  =  h  (Fig.  99). 

Proof:  Divide  the  triangle  into  three  small  triangles  PBC, 
PAC  and  PAB  by  the  dotted  lines  PA,  PE  and  PC.  Denot- 
ing the  length  of  a  side  of  the  large  triangle  by  s,  the  areas  of 
the  three  small  triangles  are  given  by  the  expressions: 

PD  PE  PF 

s    •    — ,  S    .    —  ands   .  — , 

respectively.     The  sum  of  these  areas  is  equal  to  the  total  area 
of  the  large  triangle: 

P#      PF\  _  h 

~2~    '  ~2~)  ~S    '    ^ ' 

whence  follows  the  truth  of  the  above  assertion. 

(2)  If  lines  are  drawn  through  P,  parallel  to  the  three  sides 
respectively,  viz.,  PG,  PE  and  P7,  the  relationship 

PD  :  PE  :  PF  =  PG  :  PE  :  PI 
holds,  and  further: 

PG  +  PE  +  PI  =  s. 

1  Triangular  coordinate  paper  has  recently  been  offered  for  sale  by 
SCHLEICHER  &  ScHULL,  Duren.  (The  filter  paper  manufactured  by  this 
firm  is  familiar  to  the  American  trade.  —  Trans.) 

267 


268 


THE   ELEMENTS   OF  METALLOGRAPHY. 


The  proof  is  based  upon  similarity  of  the  triangles  PDG,  PEH, 
PFI  and  AKB. 

With  the  aid  of  these  theorems,  we  are  able  to  express  the 
composition  of  a  three  component  system  according  to  weight,  or 
atomic  per  cent  by  means  of  a  point  in  the  interior  of  the  triangle. 


A/\/\A 


A  AA/  V  Y  ATVX  /\A  AAAAA7 


AAAAA'/ 


7V\ 


A/V  VV  W\  /  W  VV  VV\ 


\  AA-A  A  A/V  VV  V  VV 


AAAA/\AAAAA/VVV-VVV\AA 


AAAAAAAAAAIAAAAAA7VVVV 

G        D  K 


FIG.  99. 

The  corners  A,  B  and  C  are  intended  to  correspond  to  the 
pure  components  A,  B  and  C.  We  associate  a  point  P  with 
each  mixture  such  that  its  vertical  distance 

PD  from  the  side  BC  denotes  the  ^.-content, 

PE  from  the  side  AC  denotes  the  B-content  and 

PF  from  the  side  AB  denotes  the  C-content  of  the  mixture. 


THREE  COMPONENT  SYSTEMS.  269 

Since  PD  +  PE  +  PF  =  h,  we  obtain  the  content  in  per- 
centage figures  by  using  — —  as  a  unit  of  measure. 

-LUU 

It  follows  from  Theorem  2  that  distances  PG,  PH  and  PI, 
which  are  parallel  to  the  individual  sides,  may  be  used  as  well  in 
locating  the  composition  of  a  mixture  corresponding  to  the  point 
P  of  the  diagram.  Since  the  sum  of  these  three  distances  is 
equal  to  s,  we  must  choose  T^  of  s  as  unit  of  measure  for  per- 
centage figures  in  this  case.  The  relationship, 

PD  :  PE  :  PF  =  PG  :  PH  :  PI, 

shows  that  both  methods  of  representation  lead  to  identical 
results,  i.e.,  the  point  P  corresponds  to  the  same  mixture  in 
either  case. 

The  points  A,  B  and  C  correspond  to  pure  substances  as 
noted  above.  Therefore,  these  points  are  100  units  distant 
from  the  opposite  (respective)  sides.  The  sides  AB,  BC  and  AC 
correspond  to  binary  mixtures  of  A  and  B,  B  and  C,  and  A 
and  C,  respectively. 

We  perceive  that  the  melting-point  diagram  of  a  ternary  system 
cannot  be  drawn  on  a  plane  surface,  but  requires  a  third  dimen- 
sion for  its  construction.  To  this  end,  we  imagine  the  temper- 
ature axis  drawn  at  right  angles  to  the  plane  of  the  paper.  We 
then  obtain  a  spacial  model  of  prismatic  form,  the  three  sides  of 
which  are  formed  by  the  two  component  systems  A-B,  B-C  and 
C-A. 

§1.  THE  LIQUID  STATE  is  CHARACTERIZED  BY  COMPLETE  MISCI- 
BILITY;  THE  CRYSTALLINE  STATE  BY  COMPLETE  IMMISCI- 
BILITY. 

A.    The  Components  do  not  Unite  to  Form  a  Chemical  Compound. 

When  a  molten  alloy  consisting  of  three  components  which 
bear  the  mutual  relationship  given  in  the  above  heading  is  allowed 
to  cool,  crystallization  usually  begins  with  the  separation  of  a 
single  material.  Let  this  be  the  substance  A  in  the  present 
instance.  After  a  time,  separation  of  the  second  substance  B 
begins,  and  finally  that  of  the  third  substance  C.  From  this  time 
on,  the  melt  is  saturated  with  its  three  constituents  and  solidifies 


270 


THE   ELEMENTS   OF   METALLOGRAPHY. 


at  a  minimum  constant  temperature  without  change  in  composition, 
as  ternary  eutectic,  just  as  we  have  observed  in  the  case  of  binary 
eutectic  crystallization.  The  cooling  curve  of  a  ternary  alloy 
will,  then,  in  general,  show  two  breaks  a  and  b  (Fig.  100)  and  a 
halting  point  cd.  During  separation  of  the  component  A,  the 


Time 
FIG.  100. 

quantitative  relation  between  the  two  components  B  and  C  in  the 
melt  remains  unchanged.  The  compositions  of  such  mixtures  as 
show  constant  proportion  between  their  B-  and  C-  contents,  in 
connection  with  changing  A-  content,  are  given  by  the  points  of 
a  straight  line  drawn  through  A.  (Proof  of  this  is  taken  from 
Fig.  101.  Similarity  of  the  triangles  AP1D1  and  AP2D2,  on  the 
one  hand,  and  of  the  triangles  AP1El  and  A  P2E2,  on  the  other  hand, 


THREE  COMPONENT  SYSTEMS. 


271 


P  D      PA      P  E 

gives  rise  to  the  proportions  —j—-1  =  — l—  =  -— —  ,  from  which   the 

P2D2      P2A       PyE2 

P  D       P  D 

truth  of   the  above   assertion,  i.e.,  that— - — l  =  — ~ - ,  is  at  once 

PlEl      P2E2 

evident.) 

Thus,  the  change  in  concentration  of  the  melt  is  defined  when 
it  is  known  which  constituent  at  first  separates,  as  long  as  this 
crystalline  variety  alone  separates.  In  order  to  become  familiar 
with  subsequent  change  in  concentration,  the  concentration  of 
the  ternary  eutectic  must  first  be  ascertained.  Let  this  be  given 


E 


B 


FIG.  101. 


FIG.  102. 


by  the  point  E  in  Fig.  102.  This  is  the  concentration  at  which 
the  melt  is  saturated  with  all  three  substances,  as  we  have  seen 
above,  and  on  this  account  is  definitely  fixed,  while  here  the 
alloy  possesses  a  minimum  freezing  point.  Moreover,  let  Elt  E2 
and  Ez  represent  the  concentrations  of  the  binary  eutectics  com- 
posed of  A  and  B,  A  and  C  and  B  and  C,  respectively.  Now,  for 
example,  addition  of  C  to  the  eutectic  Elt  composed  of  A  and  B, 
will  occasion  a  lowering  of  the  melting  point  of  this  eutectic,  as 
well  as,  in  general,  a  change  in  the  proportion  of  A  to  B  in  the 
A-  and  5-saturated  melt.  The  concentration  change  sustained 
by  a  melt  which  is  already  saturated  with  two  components,  when 
increasing  amounts  of  the  third  component  are  added,  is  given 
by  the  respective  curve  EJ2,  E2E  or  E3E.  These  three  curves 
must  meet  at  the  ternary  eutectic  point,  which  represents  a  melt 
saturated  with  all  three  components.  When  the  positions  of  these 


272  THE   ELEMENTS   OF  METALLOGRAPHY. 

three  curves  are  known,  we  are  able  to  fully  determine  the  con- 
centration changes  which  a  melt  of  composition  corresponding 
to  a  point  P  (Fig.  102)  will  undergo.  Along  the  line  PD,  obtained 
by  prolongation  of  AP,  the  crystalline  variety  A  separates  from 
the  melt.  At  D,  this  line  meets  the  curve  EJ3,  giving  the  com- 
position of  melts  which  are  saturated  with  the  two  varieties  A  and 
B,  and  simultaneous  separation  of  A  and  B  follows,  with  con- 
centration change  along  the  curve  DE,  until,  at  E,  the  remainder 
of  the  melt  solidifies  without  further  concentration  change  to 
ternary  eutectic.  The  direction  of  falling  temperature  is  indi- 
cated in  Fig.  102  by  increasing  thickness  in  the  corresponding 
curves.  As  to  the  relative  amounts  of  eutectic,  we  note  that  the 
maximum  is  reached  at  Z£,  and  that  a  linear  decrease  occurs  from 
E  toward  the  sides  of  the  triangle,  where  the  zero  value  is  reached, 
there  being  only  one  or  two  components  present  in  these  local- 
ities. These  amounts  might  be  shown  graphically  by  using  a 
pyramid  of  base  ABC  and  apex  E. 

A  spacial  model,  as  given  in  Fig.  103,  is  obtained  when  the 
initial  temperatures  of  crystallization  are  entered  at  right  angles 
to  the  plane  of  the  paper.  The  three  corners  A,  B  and  C  of  the 
prism,  correspond,  as  regards  height,  to  the  melting  points  of  the 
pure  components.  The  lateral  walls  represent  three  binary 
systems,  showing  eutectics  at  the  three  concentration-temper- 
ature points  Elt  32  and  Ey  The  three  curves  E^E,  E2E  and  E3E 
which  begin  at  these  eutectic  points  correspond  to  incomplete 
equilibrium  of  two  concurrent  crystalline  varieties  with  the  melt. 
All  three  run  at  constantly  decreasing  temperature  from  the  out- 
side points  into  the  ternary  eutectic  point  E,  which,  as  we  have 
seen,  corresponds  to  complete  equilibrium  of  the  three  crystal- 
line varieties  with  melt.  At  all  temperatures  below  E,  the 
melt  is  completely  crystallized.  The  three  curves  EJZ,  E2E  and 
E3E,  along  which  a  given  pair  of  crystalline  varieties  are  in  equi- 
librium with  the  melt,  represent  the  lines  of  intersection  of  a 
respective  pair  of  surfaces,  each  of  which  characterizes  the  equi- 
librium between  a  single  crystalline  variety  and  melt.  Thus,  the 
variety  A  separates  primarily  at  some  point  upon  the  surface 
AEJZEi,  the  variety  B  at  some  point  upon  the  surface  BE^E^ 
(separated  from  the  former  surface  by  the  curve  E^E),  and  the 
variety  C  at  some  point  upon  the  surface  CE2EE3  (separated  from 


THREE  COMPONENT  SYSTEMS. 


273 


the  foregoing  surfaces  by  the  curves  E2E  and  E3E,  respectively). 
The  concentration  changes  sustained  by  a  melt  on  cooling  have 
already  been  discussed.  We  observe  that  the  curves  in  Fig.  102 
represent  projections  of  the  corresponding  spacial  curves  (in 
Fig.  103)  upon  the  concentration  plane. 


FIG.  103. 

Certain  deficiencies  are  recognized  in  the  use  of  a  spacial  model 
as  a  means  of  representing  solidification  processes  in  a  three 
component  system,  notwithstanding  the  general  view  of  asso- 
ciated details  which  it  offers.  In  particular,  the  distortions  of 
certain  regions  which  are  inevitable  when  such  a  figure  is  repre- 
sented upon  a  plane  surface  often  prove  annoying.  An  exact 
two  dimensional  representation  of  the  experimental  results  may 
be  effected  by  means  of  supplementary  plane  sections  passed 


274 


THE  ELEMENTS   OF   METALLOGRAPHY. 


through  the  three  dimensional  figure  parallel  or  perpendicular  to 
the  temperature  axis.  The  latter  method  alone  will  be  discussed 
briefly  here.  For  information  relative  to  the  form  of  sections 
parallel  to  the  temperature  axis,  reference  may  be  made  to  papers 
by  STOFFEL1  and  SAHMEN  and  v.  VEGESACK.  2  Consider  that  the 


Bi.£ 


300/4\ 

T«1  V 
7   "KX 

/           80-           xx\ 
250/-         -^         ^W 

225/-—  ^70f              XA" 
/                                                 A2500 

mr              <,  \ 

/                        >lt-                \\ 

y-             V 

*|—  —      «t-^       \  V 
£'/^W       ^€^   X 

\200° 

>*g 

7  v^^^^^r 

'  -  /\  \  f/5^  /  \ 

7         W"            ^;4 

/  \^-vy   1    />%/ 

/      ^  .v^r      x      x  v                             /             <^Yv 

^.^\^\  it       /> 

.&:  \   \.   N,  v  \    0\        / 

268°   250°       225°      200°        175°      150°    133°    150°                   175°                   200° 
E*            1 

225°  232° 

Fia.  104.     Fusion  Diagram  of  the  System  Pb-Bi-Sn, 
according  to  Charpy. 

model  shown  in  Fig.  103  be  cut  by  horizontal  planes  at  various 
heights,  and  that  the  intersecting  lines  be  projected  upon  the 
concentration  plane.  The  diagram  given  in  Fig.  104  is  constructed 

1  STOFFEL,  Z.  anorg.  Chem.,  53,  156ff.  (1907). 

2  SAHMEN  and  v.  VEGESACK,  Z.  phys.  Chem.,  59,  257,  (1907) 


THREE  COMPONENT  SYSTEMS.  275 

in  this  manner  and  constitutes  a  fusion  diagram  of  the  system 
Pb-Bi-Sn  as  determined  by  CnARPY.1  The  dotted  lines  are  lines 
of  intersection  of  the  horizontal  planes  with  the  surface  of  the 
spacial  model,  each  joining  concentrations  of  the  same  temper- 
ature of  solidification.  Hence,  they  are  called  isotherms.  The 
temperature  of  each  isotherm  is  given  by  associated  figures. 
Each  of  the  crystalline  varieties  A,  B  and  C  is  in  equilibrium  with 
an  unlimited  number  of  melts  containing  A,  B  and  C  at  any  one 
temperature,  as  indicated  by  each  respective  isotherm.  Pro- 
jections of  the  curves  EElf  EE2  and  EE3  (Fig.  103)  appear  in 
Fig.  104  as  lines  joining  the  points  at  which  two  isotherms  corre- 
sponding to  different  crystalline  varieties  intersect.  The  eutectic 
point  E  lies  at  the  concentration 

32%  Pb  -  15.5%  Sn  -  52.5%  Bi 

and  at  the  temperature  96  degrees.  This  ternary  eutectic  is  the 
well  known  Rose's  metal. 

Binary  and  ternary  (particularly  the  latter)  alloys  of  Cu,  Sn, 
Sb,  Pb,  and  Zn  are  much  used  in  the  arts  as  so-called  bearing 
metals.  The  friction  of  metal  on  metal  during  rotation  of  a 
shaft  in  its  bearings  is  not  completely  obviated  by  the  use  of 
lubricating  preparations.  An  ideal  bearing  metal  must  possess 
two  leading  characteristics.  First  of  all,  its  coefficient  of  friction 
must  be  small,  i.e.,  it  must  be  hard.  At  the  same  time  it  should 
adapt  itself  to  the  contour  of  the  revolving  shaft,  i.e.,  it  must  be 
soft  or  plastic.  Obviously  a  unit  material  cannot  possess  these 
contradictory  properties.  These  special  demands  may,  however, 
be  met  by  choosing  alloys  which  consist  of  hard  grains  embedded 
in  a  soft  ground  mass.  Charpy  (1.  c.)  was  able  to  specify  the 
concentration  limits  within  which  an  alloy  is  suitable  as  bearing 
metal,  by  means  of  microscopical  examination  in  connection  with 
determinations  of  compressibility  and  brittleness. 

B.    The  Components  when  Fused  in  Conjunction  Unite  to  Form  a 
Chemical  Compound  which  Melts  without  Decomposition. 

When  the  two  components  A  and  B  form  a  compound  AmBn 
which  melts  without  decomposition,  the  corresponding  side  wall  of 
the  fusion  figure  will  possess  the  general  form  given  in  Fig.  16c 

1  CHARPY,  Contribution  a  I'Stude  des  alliages  (1901),  p.  203. 


276 


THE   ELEMENTS   OF   METALLOGRAPHY. 


(p.  78).  The  concentrations  of  both  eutectica  are  represented  by 
the  points  El  and  EJ,  respectively,  in  Fig.  105.  Obviously,  it  is 
permissible  to  regard  the  syrtem,  Compound  AmBn  —  Component 
C,  as  a  binary  system.  Concentrations  in  this  system  are  located 
along  the  connecting  line  AmBn-C.  The  eutectic  AmBn-C  is  at  #4. 
Each  curve  in  Fig.  105  corresponds  to  equilibrium  between  two 
crystalline  varieties  and  melt.  The  direction  of  falling  temperature 
is  again  denoted  by  increasing  thickness  of  the  lines.  Two  ter- 
nary eutectica  must  be  observed  in  this  case  —  at  E  and  Ef.  The 
former  corresponds  to  the  three  crystalline  varieties  A,  AmBn 
and  C;  the  latter  to  B,  AmBn  and  C.  In  the  light  of  the  above 

information,  it  will  not  be 
difficult  to  construct  a  special 
model  covering  this  case.  In 
line  with  the  fact  stated  on 
p.  78  that  a  compound  AmBn 
corresponds  to  a  more  or  less 
rounded  maximum  on  the 
melting-point  curve  rather 
than  to  a  sharp  maximum,  the 
surface  of  the  fusion  figure 
along  AmBn-C  shows  a  more 
or  less  rounded  ridge,  sinking 
from  AmBn  to  E4,  and  then 
rising  again  towards  C.  As 

C  is  approached,  this  ridge  rises  more  sharply,  culminating  in 
a  sharp  point  at  C.  The  melting-point  diagram  may  be  sepa- 
rated into  two  independent  parts  by  division  along  the  line 
AmBn  —  C.  Each  part  corresponds  to  a  three  component  system 
without  compounds,  formed  from  the  components  AmBn,  A,  C 
and  AmBnj  B,  C,  respectively.  According  as  the  initial  concen- 
trations of  the  melts  lie  above  or  below  the  line  AmBn  —  C, 
the  compositions  of  all  phases  which  appear  during  crys- 
tallization remain  inside  either  one  or  the  other  of  the  triangles 
(AmBn)C  A  or  (AmBn)C  B.  On  this  account,  AmBn-C  may 
be  called  the  impassable  (unuberschreitbar)  line.  In  case  the 
concentration  of  the  melt  corresponds  to  a  point  upon  this  line, 
the  same  also  holds  for  the  phases  which  appear  on  cooling 
(see  above). 


FIG.  105. 


THREE  COMPONENT  SYSTEMS. 


277 


A  ternary  compound  will  not  correspond  to  a  ridge  in  the  fusion 
figure,  but  rather  to  an  isolated  conical  elevation  with  a  more  or 
less  rounded  off  summit,  according  as  the  dissociation  of  the 
fused  compound  is  more  or  less  marked.  When,  in  addition, 
binary  compounds  occur  in  large  or  small  number,  the  surface  of 
the  fusion  figure  may  appear  extremely  complicated.  Thus  far, 
investigation  of  ternary  systems  has  not  been  very  comprehensive. 
Two  ternary  inter-metallic  compounds,  viz.,  NaKHg2  and  NaCdHg, 
have  recently  been  discovered  by  Janecke.1 

§2.  BOTH  THE  LIQUID  AND  CRYSTALLINE  STATES  ARE  CHARAC- 
TERIZED BY  COMPLETE  MISCIBILITY.  —  Here,  we  will  limit  our- 
selves to  the  case  wherein  the  solidification  curves  of  the  three 
binary  systems  correspond  to 
Type  I,  according  to  Roozeboom. 
If  then,  the  three  side  walls  of 
our  prism  (Fig.  106)  show  this 
type  (given  in  Fig.  56,  p.  169), 
a  surface  passing  through  the 
three  Z-curves  will  give  the  initial 
temperatures  of  crystallization. 
Let  us  now  imagine  another  sur- 
face passed  through  the  dotted 
s-curves.  Then  we  have  before 
us  the  location  of  temperatures 
(corresponding  to  each  concentra- 
tion) at  which  the  alloys  become 
completely  solidified  (assuming 
that  equilibrium  is  established 
with  sufficient  rapidity).  In 
the  region  enclosed  by  the  two 

surfaces,  crystals  and  melt  may  exist  side  by  side.  On  cutting 
the  surfaces  by  a  horizontal  plane,  two  isotherms  ab  and  cd  are 
obtained.  Obviously,  the  former  gives  the  concentrations  of  melt 
and  the  latter  the  concentrations  of  mixed  crystals.  Special 
experiments  are  necessary  here  in  order  to  show  in  what  manner 
the  points  of  both  curves  are  associated  with  one  another,  in 
contradistinction  to  the  relations  presented  by  the  two  component 
system,  where,  in  principle,  at  least,  the  equilibrium  concentra- 

1  Janecke,  Z.  phys.  Chem.,  57,  507  (1906). 


FIG.  106. 


278  THE   ELEMENTS   OF   METALLOGRAPHY. 

tions  are  ascertained  by  simple  determination  of  the  beginning  and 
end  of  crystallization  (see  p.  172). 

No  example  for  this  case  is  known.  BoEKE1  has  constructed 
the  melting-point  diagram  for  the  system,  sodium  sulphate, 
-molybdate,  -tungstate;  but  the  behavior  of  these  substances  does 
not  correspond  to  the  simple  conditions  discussed  above,  owing 
to  appearance  of  a  minimum  and  isodimorphism,  as  well  as  to 
transformations  in  the  crystalline  state,  whereby  the  construc- 
tion of  the  fusion  figure  is  quite  complicated.  We  are  indebted 
to  ScHREiNEMAKERS2  for  a  thorough  theoretical  treatment  of 
mixed-crystal  relations  in  ternary  system. 

Finally  an  investigation  by  SAHMEN  and  v.  VEGESACKS  on  the 
occurrence  of  mixed  crystals  in  ternary  system  may  be  cited. 

§  3.  SUPPLEMENTARY.  THE  PHASE  RULE.  —  We  were  able,  in 
case  of  the  ternary  system,  to  make  the  discussion  concise,  since 
no  fundamentally  new  points  of  view  were  involved.  The 
behavior  of  an  heterogeneous  system,  i.e.,  one  composed  of  sev- 
eral phases,  on  addition  or  abstraction  of  heat,  leads  to  re- 
cognition of  two  sorts  of  equilibrium,  just  as  before.  Either 
incomplete  heterogeneous  equilibrium  or  complete  heteroge- 
neous equilibrium  may  result,  according  as  enforced  change  in 
the  heat  content  of  the  system  does  or  does  not  bring  about 
temperature  change.  We  have  seen  that  the  former  condition 
is  realized  when  at  least  one  of  the  phases  changes  its  com- 
position,4 and  that  the  latter  condition  results  when  the  com- 
position of  every  phase  remains  unchanged.  In  case  of  the  one 
component  system,  it  was  noted  that  heterogeneous  equilibrium 
is  invariably  complete,  i.e.,  the  temperature  at  which  a  unit 
crystalline  material  is  in  equilibrium  with  its  melt  is  unchange- 
able at  constant  pressure,  since  abstraction  of  heat,  for  example, 
causes  only  an  increase  in  the  amount  of  material  forming  the 
crystalline  phase,  and  a  decrease  in  the  amount  of  material  form- 
ing the  liquid  phase,  but  no  change  in  the  composition  of  either 
phase.  On  the  other  hand,  a  unit  crystalline  material  is  not  in 
complete  heterogeneous  equilibrium  with  a  melt  which  is  com- 

1  BOEKE,  Z.  anorg.  Chem.,  50,  355  (1906). 

2  SCHREINEMAKERS,  Z.  phys.  Chem.,  50,  169  (1905);  51,  547  (1905);  52, 
513  (1905). 

3  SAHMEN  and  v.  VEGESACK,  Z.  phys.  Chem.,  59,  265  (1907). 

4  Compare  in  this  connection  the  discussion  on  p.  213. 


THREE  COMPONENT  SYSTEMS.  279 

posed  of  two  substances.  We  have  met  with  many  examples  of 
this  condition. 

It  may  be  deemed  sufficient,  in  this  connection,  to  refer  again 
to  the  earlier  discussion  (cf.  p.  38  etseq.)  relative  to  the  freezing  of  a 
solution  of  common  salt.  Abstraction  of  heat  effects  concentra- 
tion of  the  solution,  at  least  at  the  start,  owing  to  separation  of 
ice,  and  attendant  lowering  of  the  freezing  temperature.  This 
persists  until  the  temperature  has  fallen  to  its  eutectic  value,  at 
which  point  salt  crystals  separate  in  common  with  ice  crystals. 
Hereby,  the  solution  is  compelled  to  solidify  without  change  of 
composition.  Thus  we  see  that,  while  two  phases  are  sufficient 
for  institution  of  complete  heterogeneous  equilibrium  in  a  one 
component  system,  three  are  necessary  in  case  of  a  two  compo- 
nent system. 

Again,  we  perceive  on  further  consideration  of  this  example 
that  the  appearance  of  a  new  phase  lessens  the  possibilities  under 
which  the  system  may  be  realized,  and,  therefore,  has  an  effect 
just  opposite  to  that  caused  by  the  entrance  of  a  new  substance 
into  the  system  (the  possibility  of  realizing  the  particular  equi- 
librium in  question  being  greater,  in  the  latter  case) .  The  two- 
phase  system,  Ice- Water,  is  realizable  at  0  degrees  only,  under 
atmospheric  pressure.  The  system,  Ice-Common  Salt  solution,  is 
realizable  between  the  limits  0  degrees  and  —  22.4  degrees,  under 
atmospheric  pressure.  This  is  a  two-phase  system,  as  is  the  former, 
but  contains  one  more  substance,  common  salt.  The  system,  Ice- 
Crystalline  Salt-Salt  solution,  on  the  other  hand,  can  exist  at  one 
temperature  only,  —  22.4  degrees,  under  atmospheric  pressure. 
The  general  limitation  of  the  range  of  existence  of  a  system,  fol- 
lowing the  appearance  of  new  phases,  is  brought  out  very  plainly 
in  the  ternary  system  shown  in  Fig.  81.  Each  surface  corre- 
sponds to  equilibrium  between  one  crystalline  variety  and  melt. 
Thus,  on  the  surface  AE^E.^  we  have  equilibrium  between  crystal- 
line A  and  melt.  Such  systems  may  be  realized  at  all  temperatures 
between  the  limits  A  and  E  in  all  concentrations  which  are  defined 
by  projection  of  the  surface  upon  the  concentration  plane.  For 
constant  temperature,  the  concentration  of  the  melt  is  in  no  way 
fixed,  but  may  vary  at  random  (see  p.  275)  within  the  values 
given  by  the  corresponding  isotherm  (Fig.  104). 

If  a  new  phase,  for  example,  the  crystalline  variety  B,  is  added, 


280  THE  ELEMENTS   OF   METALLOGRAPHY. 

the  range  of  existence  of  the  system  is  reduced  to  the  concentra- 
tions and  temperatures  given  by  a  curve  —  in  the  current  example, 
by  E^E  —  which  represents  the  line  of  intersection  of  two  sur- 
faces (each  corresponding  to  equilibrium  between  a  single  crystal- 
line variety  and  melt).  Here,  as  well,  the  equilibrium,  A  crystals- 
B  crystals-Melt,  is  realizable  at  all  temperatures  between  El 
and  E,  and  yet  the  concentration  of  the  melt  is  unequivocally 
fixed  (under  constant  pressure),  on  specification  of  the  tem- 
perature, since  this  curve  is  cut  at  only  one  point  by  a  horizontal 
plane. 

The  curve  of  incomplete  equilibrium  EtE,  along  which  three 
phases  in  the  three  component  system  are  in  equilibrium,  corre- 
sponds to  incomplete  equilibrium  in  a  two  component  system  con- 
sisting of  two  phases:  also  given  by  a  curve  (see,  for  example, 
Fig.  9b).  If  our  three  component  system  sustains  addition  of  the 
crystalline  variety  C  as  fourth  phase,  its  range  of  existence  under 
constant  pressure  is  limited  to  the  concentration  and  temperature 
of  the  point  E,  the  point  of  intersection  of  three  curves  defining  the 
equilibrium  between  a  single  crystalline  variety  and  melt.  Thus, 
at  a  given  pressure,  the  temperature  and  concentration  of  each 
phase  of  the  system  are  unequivocally  fixed,  i.e.,  complete  hetero- 
geneous equilibrium  obtains.  In  the  same  manner,  the  binary 
eutectic  is  to  be  regarded  as  the  point  of  intersection  of  two  curves 
of  incomplete  equilibrium  between  a  single  (respective)  crystalline 
variety  and  melt. 

To  summarize  then:  when  we  aggregate  the  phases  which  are 
sufficient  in  number  to  determine  complete  heterogeneous  equi- 
librium in  the  separate  systems,  we  obtain: 

For  a  one  component  system 2  phases, 

For  a  two  component  system 3  phases, 

For  a  three  component  system 4  phases, 

and  we  conclude  that  n  +  1  phases  are  sufficient  in  an  n-compo- 
nent  system  for  the  production  of  cpmplete  heterogeneous  equi- 
librium. l 

1  Under  certain  conditions  (see  p.  165  et  seq.~),  it  is  possible  for  complete 
heterogeneous  equilibrium  to  occur  in  a  two  component  system,  for  example, 
when  only  two  phases  are  present.  Such  a  system  is  therefore  to  be  regarded 
as  a  one  component  system  throughout  the  temperature  and  concentration 
ranges  in  question  (cf.,  in  this  connection,  p.  34  et  seq.}. 


THREE  COMPONENT  SYSTEMS.  281 

These  equilibria  which  we  have  considered  have  been  limited, 
for  the  most  part,  to  such  as  are  made  up  of  liquid  or  crystalline 
phases.  Change  of  pressure  has  relatively  little  influence  upon 
such  equilibria,  and  we  are  therefore  justified  in  neglecting  the 
effects  of  not  too  great  pressure  changes.  This  has  been  done  by 
regarding  the  pressure  as  constant.  If,  however,  we  vary  the 
pressure  within  wide  limits  —  by  hundreds  or  thousands  of  at- 
mospheres —  the  resulting  effect  upon  the  melting  temperature, 
for  example,  will  be  quite  considerable.  Hence,  such  complete 
heterogeneous  equilibrium  is  not  immune  from  all  possibility  of 
change,  inasmuch  as  we  may  change  the  pressure  exerted  upon  the 
system,  and  thereby  effect  a  simultaneous  change  in  the  equilib- 
rium temperature.  We  know  from  previous  experience  that  the 
appearance  of  a  new  phase  invariably  limits  the  range  of  existence 
of  the  system,  and  we  find  ourselves  in  agreement  with  both  theory 
and  practice  when  we  urge  that  for  an  n-component  system  which 
consists  of  n  +  2  phases  the  pressure  is  definitely  fixed  and  that, 
in  consequence,  the  system  is  not  open  to  alteration,  or,  more 
accurately,  that  any  change  must  cause  disappearance  of  a  phase. 
Since  the  range  of  existence  of  such  a  completely  defined  system 
with  respect  to  pressure,  temperature  and  composition  of  the 
separate  phases  is  the  smallest  imaginable,  any  further  limitation 
of  this  range,  such  as  would  characterize  appearance  of  another 
phase,  cannot  be  effected.  Thus  we  see  that,  in  an  n-component 
system,  not  more  than  n  -f  2  phases  can  exist  side  by  side.  Indeed, 
these  are  capable  of  coincident  existence  only  at  a  certain  defined 
temperature  and  under  an  equally  specific  pressure,  as  has  been 
said  before. 

Equilibrium  between  the  three  states  of  aggregation  of  a  pure 
substance,  for  example,  water,  may  be  cited  as  a  simple  example 
of  equilibrium  in  an  n-component  system,  consisting  of  n  +  2 
phases.  We  know  that  under  atmospheric  pressure  the  equilib- 
rium temperature  for  Ice-Liquid  Water  is  0  degrees,  and  that  the 
melting  point  of  ice  is  lowered  by  increase  in  pressure  at  the  rate  of 
0.0077  degrees  per  atmosphere  (see  p.  7).  Thus,  the  freezing 
temperature  of  water  under  a  pressure  of  100  atmospheres  will  be 
—  0.77  degrees.  The  complete  heterogeneous  equilibrium,  Ice- 
Liquid  Water,  may,  therefore,  be  realized  at  various  temperatures, 
provided  the  pressure  attains  a  corresponding  value.  The  pres- 


282  THE   ELEMENTS   OF   METALLOGRAPHY. 

sure  becomes  definite  on  specification  of  the  temperature,  and 
the  temperature  on  specification  of  the  pressure.  If,  how- 
ever, water  vapor  is  included  as  an  additional  phase,  the  above 
possibility  of  change  is  no  longer  admissible.  Ice,  liquid  water 
and  water  vapor  are  capable  of  coexistence  at  the  one  temperature, 
+  0.0077  degrees,  and  under  the  one  pressure,  4.57  mm.  (the  pres- 
sure of  saturated  water  vapor  at  this  temperature).  (The  insig- 
nificance of  this  pressure  in  comparison  with  normal  atmospheric 
pressure  is  responsible  for  the  fact  that  the  equilibrium  temperature 
rises  practically  as  far  above  0  degrees  as  would  correspond  to  a 
pressure  change  of  one  atrriosphere.) 

Evidence  contradictory  to  the  above  statements  seems  to  lie 
in  the  observation  that  the  equilibrium  Ice-Liquid  water-Water 
Vapor  may  be  realized  in  a  (non-evacuated)  space  filled  with  an 
indifferent  gas  —  air,  for  example  —  under  a  pressure  of  one  atmos- 
sphere  —  moreover,  at  the  temperature  0  degrees  in  this  case, 
corresponding  to  the  current  pressure  value  of  one  atmosphere. 
This  apparent  contradiction  finds  an  explanation  in  the  fact  that 
air  takes  part  in  the  equilibrium  not  only  in  the  gas  phase,  but 
also  in  the  crystalline  and  liquid  phases.  The  ice,  as  well  as  the 
liquid  water,  will  have  dissolved  quantities  of  each  gas  present,  in 
proportion  to  the  partial  pressures  of  these  gases,  whereby  we 
must  of  necessity  recognize  as  many  independent  constituents 
(components),  in  addition  to  the  water,  as  there  are  gases  present. 
Thus,  on  these  grounds,  there  is  no  such  thing  as  an  indifferent 
gas,  i.e.,  one  whose  presence  may  be  entirely  neglected. 

This  explanation  indicates  that,  before  making  general  appli- 
cation of  deductions  from  the  phase  rule,  certain  idealisms  must 
be  made  regarding  our  experimental  appointments,  provided  the 
fusion  experiments  are  not  carried  out  in  a  vacuum,  but  in  open 
crucibles  (which  communicate  freely  with  the  atmosphere),  as  is 
usually  the  case.  Two  assumptions  may  be  made  in  this  connec- 
tion. The  first  is  that  the  presence  of  air  be  neglected,  and  that 
we  work  in  a  vacuum,  whereby  the  system  must  exist  strictly 
under  the  pressure  due  to  its  own  vapor.  If,  for  example,  we 
have  a  solidifying  eutectic  mixture  of  two  metals  in  our  vessel, 
there  is  present,  besides  the  three  phases,  Crystalline  A,  Crystalline 
B  and  Melt,  a  fourth  or  gas  phase,  and  we  perceive  that,  accord- 
ing to  the  rule  previously  given,  in  this  system  where  n  =  2,  a 


THREE  COMPONENT  SYSTEMS.  283 

greater  number  of  phases  cannot  be  present  at  the  same  time. 
Pressure  (equal  to  the  sum  of  the  partial  pressures  of  the 
substances  concerned),  temperature  and  individual  composition 
of  the  several  phases  are  completely  fixed,  according  to  the 
above,  and  cannot  be  altered,  unless  accompanied  by  the  dis- 
appearance of  one  of  the  phases.  Such  a  system  is  frequently 
termed  a  " non-variant  system"  in  the  literature,  for  obvious 
reasons. 

In  terms  of  the  second  assumption  bearing  upon  this  question, 
we  imagine  the  surface  of  the  melt  to  be  protected  from  contact 
with  the  atmosphere  by  means  of  a  perfectly  articulating  and 
impervious  piston.  The  atmospheric  pressure,  which  operates 
upon  the  piston  from  above,  may  then  be  regarded  simply  as 
mechanical  pressure  directed  against  the  system.  Thus,  the 
gas  phase  is  assumed  to  be  entirely  absent.  Previous  conclusions 
have  been  based  upon  this  conception.  Considering  the  binary 
eutectic  from  this  standpoint,  we  see  that  equilibrium  is  complete. 
There  are  n(=2)  +  l  =  3  phases  participating,  namely,  Crys- 
talline A,  Crystalline  B  and  Melt.  A  definite  mechanical  pressure 
is  exerted  upon  the  system,  change  of  which  within  certain  limits 
causes  a  shifting  of  the  equilibrium  temperature,  without  coin- 
cident disappearance  of  any  phase  from  the  system. 

Both  conceptions  "idealize  "  i.e.,  they  presume  other  experi- 
mental conditions,  than  those  which  are  actually  observed.  Never- 
theless, the  data  to  be  obtained  under  actual  working  conditions 
differ  so  slightly  from  those  which  would  be  realized  under  the 
strictes  tpossible  adherence  to  one  or  the  other  of  the  ideal  pro- 
cedures that  we  need  pay  no  attention  to  the  above  imaginary 
restrictions  in  considering  experimental  results.  When  possible, 
experiments  are  conducted  in  the  medium  of  a  gas  which  is  prac- 
tically without  chemical  action  upon  the  melt.  It  has  already 
been  stated  (on  p.  7)  that  a  change  of  more  than  0.03  degree 
in  melting  point  per  atmosphere  pressure  change  has  not  as  yet 
been  observed. 

We  have  thus  arrived  at  the  result  that,  neglecting  the  gas 
phase,  the  greatest  number  of  phases  which  may  be  present  in  an 
n-component  system  is  n  +  1.  If  they  are  all  present  at  the 
same  time,  addition  or  abstraction  of  heat  under  constant  pres- 
sure can  occasion  no  temperature  or  concentration  change,  but 


284  THE  ELEMENTS   OF   METALLOGRAPHY. 

merely  change  in  the  respective  amounts  of  the  several  phases. 
Not  until  a  phase  is  completely  exhausted  does  further  change  in 
the  heat  content  of  the  system  effect  concentration  change  —  in 
at  least  one  phase  —  accompanied  by  change  in  the  equilibrium 
temperature.  It  is  clear  that  adequate  appreciation  of  these 
relations  effectually  simplifies  the  study  of  equilibrium  conditions. 
Thus  we  are  able,  even  though  unfamiliar  with  the  actual  process 
of  crystallization,  to  affirm  that  simultaneous  separation  of  two 
crystalline  varieties  from  a  melt  consisting  of  both  substances 
(eutectic  crystallization  in  a  two  component  system)  must  proceed 
at  constant  temperature,  since  here,  n  (=  2)  +  1  =  3  phases, 
namely  both  crystalline  varieties  and  melt,  are  in  equilibrium.  We 
also  see  that  crystallization  at  constant  temperature  will  not  result 
in  a  three-component  system  until  four  phases  are  in  equilibrium 
with  one  another,  as  is  true  during  the  solidification  of  a  ternary 
eutectic.  In  the  case  representing  incomplete  miscibility  in 
the  liquid  state  and  complete  immiscibility  in  the  crystalline 
state  (discussed  on  p.  149),  complete  heterogeneous  equilibrium, 
viz.,  constant  temperature,  must  result  at  the  time  when  a  crys- 
talline variety  appears  in  the  presence  of  the  two  liquid  phases. 
But  it  is  never  possible  for  two  crystalline  varieties  to  appear  in 
the  presence  of  both  liquid  phases,  since,  in  such  event,  the  number 
of  hypothetical  coexistent  phases  would  be  one  too  great. 

Knowledge  of  the  above  principles  aids  us  materially  in  criti- 
cising the  structure  of  solidified  alloys.  Coexistence  of  n  + 1 
liquid  or  crystalline  phases  is  possible  only  at  the  temperature 
of  equilibrium  under  the  prevailing  pressure.  If  the  system  is 
existent  at  a  lower  temperature,  one  of  the  phases  must  have 
become  exhausted.  Thus,  a  two  component  system  in  equilib- 
rium in  the  solid  condition  can  show  in  maxima  two  crystalline 
varieties;  a  three  component  system,  three  varieties.  If  more 
are  present,  we  are  dealing  with  abnormal  structure,  due  to  in- 
complete reaction  (see  pp.  134,  138).  Equilibrium  is  not  at  hand 
in  such  a  system.  An  exception  to  the  above  could  obtain  only 
when  the  temperature  at  which  the  sections  were  under  examina- 
tion chanced  to  coincide  with  a  temperature  of  complete  hetero- 
geneous equilibrium.  This  conjecture  might  be  tested,  omitting 
from  consideration,  however,  the  circumstance  that  in  general 
no  further  changes  in  the  sections  occur  at  ordinary  temperature, 


THREE  COMPONENT  SYSTEMS.  285 

on  the  grounds  that  slight  cooling  or  heating  would  of  necessity 
cause  the  disappearance  of  one  or  two  structure  elements. 

The  relations  which  have  been  outlined  above  are  special  cases 
of  a  general  law  developed  by  GIBBS  l  on  theoretical  grounds;  the 
so-called  Phase  Rule,  according  to  which  the  number  of  Degrees 
of  Freedom  (=  possibilities  of  change)  F,  the  number  of  com- 
ponents n,  and  the  number  of  phases  P,  corresponding  to  equilib- 
rium in  a  given  system,  are  mutually  related  as  follows: 

F  =  n  +  2  -P. 

We  see,  on  consideration  of  this  equation,  that  the  appearance 
of  a  new  phase  robs  this  system  of  one  possibility  of  change,  or 
Degree  of  Freedom.  Since  F  cannot  assume  a  negative  value, 
the  greatest  possible  number  of  coexistent  phases  (inclusive  of 
the  gas  phase)  is  n  +  2.  The  above  relation  holds  under  an 
assumption  that  the  system  is  in  equilibrium,  whereby  a  suffi- 
ciently rapid  rate  of  reaction  throughout  all  transformation  is 
presumed. 

1  GIBBS,  Thermodynamische  Studien  (German  translation  by  Ostwald), 
Leipzig,  1892  P.  115.  Trans.  Coun  Acad.,  iii,  1875-8. 


PART   H. 
PRACTICE, 


287 


CHAPTER  I. 
THERMAL   INVESTIGATION. 

§  1.    MEASUREMENT  OP  TEMPERATURE. 

THE  use  of  thermometers  based  upon  the  expansion  of  liquids 
is  not  considered  in  this  connection.  Thermo-elements,  or  thermo- 
electric couples,  are  best  suited  to  temperature  measurement  in 
metallographical  work.  Small  dimensions  may  be  chosen  at  will 
in  their  construction.  Thus,  they  are  more  sensitive  than  mercury 
thermometers  in  small  masses  of  material  on  account  of  their  less 
rapid  conduction  of  heat  away  from  the  surrounding  mixture. 
For  this  reason,  they  are  preferable  to  thermometers  in  which  a 
liquid  column  is  used,  even  at  temperatures  which  are  low  enough 
to  permit  application  of  the  latter  type. 

Thermo-electric  temperature  measurement  is  based  upon  deter- 
mination of  the  electromotive  force  between  the  free  ends  of  two 
metallic  wires  of  different  composition,  the  other  ends  being  fixed 
in  secure  contact  and  heated  to  the  questionable  temperature. 
The  junction  is  usually  in  the  form  of  a  small  bead  of  metal, 
obtained  by  fusing  the  ends  of  the  wires  together.  The  differ- 
ence in  temperature  between  the  junction  and  the  free  ends  bears 
a  functional  relation  to  the  observed  electromotive  force.  If  this 
relation  is  known,  together  with  the  temperature  of  the  free  ends, 
measurement  of  the  electromotive  force  supplies  the  data  neces- 
sary for  calculation  of  the  temperature  of  the  junction.  For  the 
temperature  interval  between  —  200  degrees  and  +  600  degrees, 
thermo-elements  giving  relatively  large  electromotive  forces  for 
small  temperature  differences  may  be  advantageously  used.  A 
couple  consisting  of  copper  or  iron  joined  to  a  constant  is  often 
used  for  this  purpose.  For  measurements  between  +200  degrees 
and  + 1600  degrees  the  LeChatelier  thermo-element,  in  which  one 
wire  is  of  pure  platinum  and  the  other  of  a  platinum-rhodium 
alloy  (platinum  90  per  cent  —  rhodium  10  per  cent),  is  almost 
universally  used.  (A  thermo-element  of  pure  iridium  and  an 

289 


290 


THE   ELEMENTS   OF   METALLOGRAPHY. 


alloy  of  iridium  with  10  per  cent  ruthenium  may  be  used  up 
to  about  2000  degrees).  Thermo-elements  with  accompanying 
tables  giving  the  electromotive  force  as  function  of  the  temper- 
ature, determined  at  the  Physikalisch-Technische  Reichsanstalt, 
are  on  the  market  at  the  present  time.  The  relation  between 


18 

ir 

16 
15 
14 

42  13 


£    8 


0   100   200  300   400  500  600  700   800  900  1000  1100  1200  1300  1400  1500  1600  1700 

Temperature  difference  of  the  Junction  in  Degrees 
FIG.  107. 

electromotive  force  and  temperature  of  the  junction  for  a  LeCha- 
telier  thermo-element,  the  free  ends  of  which  were  maintained  at 
0  degrees,  is  shown  graphically  in  Fig.  107  according  to  measure- 
ments by  HOLBORN  and  DAY.1  The  horizontal  axis  is  graduated 
in  centigrade  temperatures,  the  vertical  axis  in  millivolts.  It 
may  be  observed  that  the  electromotive  force  is  not  directly  pro- 
portional to  the  temperature,  on  the  contrary,  its  increase  per  100 

1  HOLBORN  and  DAY,  Drude's  Ann.,  (2)  505  (1900). 


THERMAL  INVESTIGATION.  291 

degrees  temperature  difference  is  about  twice  as  great  at  higher 
temperatures  as  at  lower  temperatures.  Between  250  degrees 
and  1100  degrees  Holborn  and  Day  (1.  c.),  were  able  to  represent 
the  relation  between  electromotive  force  and  temperature  with 
great  accuracy  by  means  of  a  quadratic  interpolation  formula. 
Temperatures  were  measured  with  an  air  thermometer  up  to 
1130  degrees.  Above  this  point,  no  determinations  were  made, 
the  further  course  of  the  curve  as  represented  resting  upon  the 
assumption  that  their  interpolation  formula  remain  accurate 
outside  of  verified  limits.  LUMMER  and  PmNGSHEiM1  uphold 
this  assumption  as  a  result  of  their  investigation  on  the  laws  of 
black  body  radiation.2 

Electromotive  forces  are  measured  with  a  galvanometer,  the 
scale  of  which  is  advantageously  graduated  in  degrees  centigrade 
corresponding  to  the  LeChatelier  thermo-element  with  free  ends 
at  0  degrees,  as  well  as  in  millivolts.  This  arrangement  is 
extremely  convenient,  as  it  obviates  considerable  calculation. 
Since  the  deflection  of  the  needle  is  proportional  to  the  electro- 
motive force,  the  divisions  on  the  temperature  scale  become  larger 
as  the  temperature  increases.  The  requisites  of  an  instrument 
of  this  sort  are  rapid  adjustment,  extreme  sensitiveness,  and 
large  internal  resistance,  in  comparison  with  which  the  resistance 
in  the  outside  circuit  is  negligible.  The  millivoltmeters  con- 
structed for  this  purpose  by  the  firm  of  SIEMENS  and  HALSKE, 
Berlin,  possess  an  internal  resistance  of  approximately  400  ohms 
and  a  sensitiveness  of  0.1  millivolts  per  degree  (=  0.8  mm.), 
deflection.  These  are  DEPREZ-D'ARSONVAL  galvanometers,  con- 
sisting of  a  spool,  through  which  the  current  to  be  measured 
flows,  suspended  in  the  field  of  a  strong  magnet.  The  instru- 
ment (Fig.  108)  is  levelled  by  means  of  the  three-foot  screws 
upon  a  support  which  should  be  free  from  vibration.  After  releas- 
ing the  needle  arrest,  the  pointer  should  register  0.  Trifling  varia- 
tions from  the  0  point  may  be  corrected  by  manipulation  of  the 

1  LUMMER  and  PRINGSHEIM,  Physik.  Z.,  3,  98  (1901). 

2  The  validity  of  this  extrapolation  is  questioned  in  a  recent  paper  by 
HOLBORN  and  VALENTINER,  Drude's  Ann.,  (4)  22,  1  (1907).     These  authors 
have  made  direct  use  of  the  air  thermometer  in  connection  with  the  ther- 
moelement up  to  1600  degrees.     Since  their  results  necessitate  a  revision  of 
the  generally  accepted  value  of  one  of  the  radiation  constants  (in  Wien's  equa- 
tion), they  are  not  considered  here. 


292 


THE   ELEMENTS   OF   METALLOGRAPHY. 


adjusting  screw  at  the  head  of  the  suspension.  If  the  variation  is 
greater  than  two  scale  divisions,  proper  adjustment  is  no  longer 
possible,  and  the  instrument  must  be  repaired.  Before  trans- 
portation, care  must  be  exercised  that  the  needle  is  in  arrest. 

Only  when  the  instrument  is  in  use, 
should  the  needle  remain  in  sus- 
pension. The  zero  point  is  affected 
by  temperature  changes.  If  read- 
ings must  be  made  in  close  prox- 
imity to  a  source  of  heat,  the 
galvanometer  should  be  protected 
as  far  as  possible  by  several  sheets 
of  asbestos. 

Quite  recently,  the  firm  of 
Siemens  and  Halske  has  placed  a 
modified  form  of  instrument  on  the 
market,  which  is  adapted  to  a 

larger  range  of  temperature  measurement.  This  is  secured  by 
introducing  two  separate  resistances  of  approximately  400  and 
130  ohms,  respectively,  either  of  which  may  be  used  by  changing 


FIG.  108. 


FIG.  109. 

the   connection.     A  temperature   scale  for  each  connection   is 
given,  and  the  millivolt  graduations  are  omitted. 

A  small  oxy-hydrogen  flame  is  most  satisfactory  for  joining  the 
two  ends  of  the  LeChatelier  thermo-element.  The  junction  is 
shown  at  L  in  Fig.  109.  In  the  Goettingen  laboratory,  thin 


THERMAL  INVESTIGATION.  293 

thermoelement  wires  (of  0.2  mm.  diameter),  are  used,  partly  on 
account  of  reduced  expense,  and  partly  by  reason  of  the  minimum 
heat  conduction  from  the  melt  which  can  be  secured  in  this  way. 
The  thermo-element  junction  is  protected  from  contact  with  the 
molten  metal  by  placing  it  in  a  small  tube  of  unglazed  porcelain 
(inside  diameter  1.7  mm.,  outside  diameter  2.5  mm.,  length 
15  cm.)  closed  at  the  lower  end  by  fusion  in  the  oxy-hydrogen 
flame.  This  material  may  be  obtained  from  the  Royal  Porcelain 
Manufactory  in  Berlin.  For  temperatures  below  800  degrees 
this  tube  may  be  made  of  difficultly  fusible  glass,  e.g.,  Jena  com- 
bustion tubing.  (A  tube  of  this  sort,  which  hinders  heat  transfer 
between  melt  and  thermo-element,  is  undesirable  except  when 
absolutely  necessary.  For  work  with  non-metallic  substances 
which  do  not  attack  the  thermo-element  wires,  it  may  often  be 
omitted).  Insulation  of  the  two  wires  inside  the  protecting  tube 
is  conveniently  effected  by  means  of  thin  mica  strips.  A  better 
arrangement  is  obtained  by  enclosing  one  of  the  wires  with  a 
capillary  tube  of  porcelain,  or  of  other  refractory  material. 
Material  manufactured  for  use  in  the  Nernst  lamp  has  served  this 
purpose  in  the  Goettingen  laboratory.  Short  pieces  of  0.3  mm. 
inside  and  1  mm.  outside  diameter  in  sufficient  quantity  to 
perfect  insulation  inside  the  protecting  tube  are  very  satis- 
factory. 

Both  free  ends  of  the  thermo-element  are  connected  with 
heavy  copper  wires  by  means  of  binding  posts.  These  copper 
wires  lead  to  the  voltmeter  D.  The  binding-post  connections 
are  enclosed  in  test  tubes  and  placed  in  a  beaker  C  containing 
water.  A  thermometer  measures  the  temperature  of  the  bath 
(free  ends  of  the  thermo-element),  which  may  be  varied  at  will, 
or  maintained  at  0°  C.  by  adding  ice.  Attention  has  been  called 
to  the  fact  that  the  electromotive  force  measures  the  tempera- 
ture difference  between  the  junction  and  the  free  ends  of  the 
thermo-element.  Consequently,  the  voltmeter  registers  the  true 
temperature  of  the  junction  only  when  the  free  ends  are  main- 
tained at  0  degrees.  If  the  temperature  of  the  free  ends  is 
t  degrees  (measured  by  the  temperature  of  the  water  in  the 
beaker  C),  the  electromotive  force  corresponding  to  the  differ- 
ence between  0  degrees  and  t  degrees  must  be  added  to  the  read- 
ing from  the  instrument  to  obtain  the  total  electromotive  force 


294 


THE  ELEMENTS   OF  METALLOGRAPHY. 


corresponding  to  the  true  temperature  of  the  junction.     It  is 
more  convenient  to  use  the  following  table  prepared  by  VOGEL:  * 


TABLE  7. 


Temperature  reading 
of  the  voltmeter  in 
degrees. 

P 

0 

1 

100 

0.89 

200 

0.76 

300 

0.65 

400 

0.59 

500 

0.56 

600 

0.54 

700 

0.52 

800 

0.51 

900 

0.50 

1000 

0.49 

The  temperature  of  the  free  ends  is  observed,  multiplied  by 
the  factor  p,  taken  from  Table  7,  and  added  to  the  temperature 
reading  of  the  voltmeter.  This  gives  the  actual  temperature  of 
the  junction.  The  decrease  in  value  of  the  factor  p  corresponds 
to  the  increase  in  electromotive  force  per  degree  (Fig.  85)  with 
rising  temperature.  At  temperatures  above  500  degrees,  sufficient 
accuracy  is  obtained  by  placing  p  =  J.  This  correction  applies 
to  the  LeChatelier  thermo-element  only.  Corrections  for  the 
copper-constantan  thermo-element  may  be  made  by  adding  the 
total  temperature  of  the  free  ends  to  the  observed  temperature, 
since  with  this  element  the  electromotive  force  is  approximately 
proportional  to  the  difference  in  temperature  between  the  free 
ends  and  the  junction  throughout  its  whole  range  of  usefulness. 

It  is  necessary  to  standardize  the  thermo-element  before  use. 
Where  wires  as  small  as  0.2  mm.  thickness  are  used  in  its  con- 
struction, as  is  often  desirable  in  metallographical  work,  standard- 
ization is  not  undertaken  at  the  Physikalisch-technische  Reich- 
sanstalt.  Moreover,  since  it  is  essential  that  the  readings  of  the 
instrument  be  frequently  tested  for  accuracy,  a  short  description 
of  the  method  of  calibration  is  hereby  presented.  For  this  pur- 
1  VOGEL,  Z.  anorg.  Chem.,  45,  13  (1905). 


THERMAL  INVESTIGATION.  295 

pose,  the  melting  points  of  the  following  metals   (in  pure  con- 
dition) are  used  as  fixed  points: 

Lead 326.91 

Antimony 630.61 

Gold 1064.1 

Nickel 1451. 2 

Palladium 1541.3 

Lead,  antimony  and  nickel  of  adequate  purity  may  be  obtained 
from  the  firm  of  C.  A.  F.  Kahlbaum,  Berlin.  The  melting  points 
are  determined  in  the  usual  manner  by  taking  cooling  curves. 
This  method  may  also  be  chosen  for  the  gold  and  palladium 
calibrations.  On  account  of  the  attendant  expense,  however,  the 
so-called  wire  method l  is  usually  preferred.  This  procedure  con- 
sists in  fusing  a  short  piece  of  the  metal  in  question  between  the 
two  wires  of  the  thermo-element,  in  place  of  the  ordinary  junction, 
heating  this  part  gradually  up  to  the  fusing  temperature  of  the 
wire,  and  continually  observing  the  temperature  up  to  the  point 
where  contact  is  broken  by  fusion.  This  temperature  is  the 
melting  point  sought.  It  sometimes  happens  that  the  molten 
drop  of  metal  remains  suspended  between  the  wires  for  a  short 
time,  keeping  the  circuit  closed  after  fusion,  and  failing  to  drop 
away  until  a  temperature  higher  than  the  temperature  of  fusion 
has  been  reached.  This  method  is  applicable  to  none  but  the 
noble  metals,  which  are  not  oxidized  in  air,  and  not  even  to 
these  if  their  melting  points  are  lowered  by  the  material  of  the 
thermo-element.  In  any  case,  if  a  sufficient  quantity  of  material 
(approximately,  20-30  g.)  is  at  hand,  the  crucible  method  (by 
which  cooling  curves  are  taken  in  the  usual  manner)  is  to  be  pre- 
ferred, since,  aside  from  added  certainty  and  accuracy,  no  sepa- 
ration of  the  two  ends  of  the  thermo-element  is  required. 

Results  agreeing  within  5  degrees  may  be  regarded  as  satis- 
factory. It  may  also  be  noted  in  this  connection  that  the  use  of 
copper  for  calibration  purposes  cannot  be  highly  recommended, 

1  HOLBORN  and  DAY,  Drude's  Ann.  (4),  2,  535  (1900). 

2  RUER,  Z.  anorg.  Chem.,  51,  225  (1906). 

3  NERNST  and  v.  WARTENBERG,  Verhandlungen  der  deutschen  physikal- 
ischen  Gesellschaft,  8  (1906),  p.  48. 


296  THE   ELEMENTS   OF   METALLOGRAPHY. 

since,  according  to  HEYN/  the  molten  metal  dissolves  copper 
suboxide  (formed  when  air  is  incompletely  excluded),  thereby 
forming  an  eutectic  which  is  fusible  some  20  degrees  lower  than 
the  true  melting  point  of  the  pure  metal.  According  to  CALLEN- 
DER  and  HEYCOCK  and  NEVILLE  silver  melts  and  solidifies  in  an 
oxidizing  atmosphere  at  a  lower  temperature  than  in  a  reducing 
atmosphere.2  The  melting  points  of  lead,  antimony  and  gold 
maybe  regarded  as  very  definitely  fixed.  The  above  determination 
of  the  melting  point  of  nickel  (1451  degrees)  is  based  upon  the  pal- 
ladium melting  point,  1541  degrees.  The  recent  measurements  of 
Holborn  and  Valentiner  place  this  point  at  1575  degrees.  Ac- 
ceptation of  this  figure  forces  a  rejection  of  the  previously  used 
interpolation  formula,  based  upon  thermo-electric  measurements, 
and  necessitates  the  introduction  of  extremely  inconvenient  correc- 
tions. Until  this  question  is  settled  beyond  controversy,  it  seems 
desirable  to  use  the  value  1541  degrees  for  the  palladium  point. 
The  temperature  interval  above  1100  degrees,  as  defined  by  the 
above  fixed  points,  is,  therefore,  subject  to  possible  revision  on 
the  basis  of  future  work. 

The  metals  chosen  for  calibration  of  the  thermo-element 
obviously  depend  upon  the  temperature  range  throughout  which 
it  is  to  be  used.  Corrections  throughout  the  whole  range 
become  approximately  linear  if  the  palladium  point  is  placed  at 
1546  degrees;  consequently,  two  fixed  points  suffice  in  the  prep- 
aration of  a  complete  correction  table  —  perhaps  supplemented 
by  an  additional  point  for  extra  control.  A  thermo-element  may 
be  adequately  tested  for  accuracy  by  determination  of  a  single 
fixed  point.  The  gradual  decrease  in  length  to  which  a  thermo- 
element is  subjected  through  long-continued  usage  (accident,  etc.) 
is  itself  responsible  for  a  certain  variation  in  the  temperature 
corresponding  to  a  given  electromotive  force,  if  the  instrument 
is  constructed  of  thin  wires,  as  described  above.  The  resistance 
of  such  a  thermo-element,  each  wire  of  which  measures  1  meter, 
is  approximately  9  ohms  at  ordinary  temperature.  If  the  thermo- 
element is  reduced  to  half  length,  its  total  resistance  will  have 

1  HEYN,  Mittheilungen  der  Koenigl.     Technischen  Versuchsanstalt,  Ber- 
lin, 315  (1900). 

2  HEYCOCK  and  NEVILLE,  Jour.  Chem.  Soc.,  1895,  p.  160, 1024;  HOLBORN 
and  DAY,  Drude's  Ann.  (4),  2,  528  (1900) 


THERMAL  INVESTIGATION.  297 

decreased  one-half,  whereby,  in  a  circuit,  the  total  resistance  of 
which  measures  450  ohms,  an  increase  in  the  observed  electro- 
motive force  (and  consequently  in  the  observed  temperature)  of 
about  1  per  cent  is  attained.  Nevertheless,  it  seems  that  this  is 
not  the  only  reason  for  the  well-recognized  variation  in  electro- 
motive force  which  is  incident  to  renewal  of  the  junction.1  It 
is  apparently  difficult  to  prepare  such  exceedingly  thin  wires  in 
a  state  of  perfect  homogeneity. 

Certain  gases  such  as  sulphur  vapor,  phosphorus  vapor,  etc., 
attack  the  thermo-element  strongly,  rendering  it  brittle  and 
unreliable  in  its  registry.  This  applies,  as  well,  to  the  effect  of 
hydrogen  at  temperatures  above  1200  degrees.  On  this  account, 
use  of  hydrogen  to  guard  against  oxidation,  above  this  tempera- 
ture, cannot  be  recommended,  since  diffusion  through  the  porce- 
lain protecting  tube  is  sure  to  result  with  attendant  damage  to 
the  thermo-element.  On  the  other  hand,  when  nitrogen  is  used 
it  is  difficult,  without  taking  especial  precautions,  to  prevent 
access  of  air  and  consequent  oxidation  of  a  melt  easily  sus- 
ceptible to  this  sort  of  chemical  action.  This  disadvantage  is 
unusually  troublesome  when  the  resulting  oxide,  as  in  the  case 
of  manganese  and  silicon,  attacks  porcelain  strongly.  In  such 
cases,  the  porcelain  protecting  tube  is  usually  destroyed.  LEVIN 
and  TAMMANN2  protect  the  thermo-element  with  a  layer  of  mag- 
nesia. This  material  cannot  be  placed  directly  in  contact  with 
porcelain,  since  an  easily  fusible  compound  will  then  be  formed 
at  high  temperatures.  Accordingly,  the  protecting  tube  is  first 
covered  with  a  thin  layer  of  nickel  or  platinum  upon  which  the 
magnesia  mass,  consisting  of  magnesia  and  a  quantity  of  ground 
porcelain,  made  into  a  paste  with  a  solution  of  tragacanth  and 
dextrine,  is  placed,  leaving  the  upper  part  of  the  nickel  or 
platinum  foil  free.  This  tube  is  dried  in  the  air  and  ignited  to 
approximately  1400  degrees  before  use.  The  tube,  protected  in 
this  manner,  lasts  through  one  or  more  experiments,  but  we  are 
here  confronted  with  the  disadvantage  of  imperfect  heat  trans- 
fer between  the  heavily  enveloped  thermo-element  and  melt, 
which  renders  the  reading  of  temperature  less  sensitive  and 
definite  than  is  to  be  desired.  The  use  of  nitrogen,  and  i 

1  HOLBORN  and  DAY,  Drude's  Ann.  (4),  2,  540ff.  (1900). 

2  LEVIN  and  TAMMANN,  Z.  anorg.  Chem.,  47,  136  (1905). 


298 


THE   ELEMENTS   OF   METALLOGRAPHY. 


duction  of  the  ther mo-element,  protected  in  the  usual  manner,  at 
the  last  moment  before  taking  the  cooling  curve  will  be  found 
practicable  in  most  cases.  Thus  far,  tubes  of  pure  magnesia  have 
not  given  satisfaction. 

§  2.    HEATING    APPARATUS   FOR   THE    PREPARATION    OF 
FUSED  ALLOYS. 

A.    For  Temperatures  up  to  1100  Degrees. 

Small  Hessian  crucibles  are  used  as  receptacles  whenever  possi- 
ble, owing  to  their  cheapness.  In  general,  individual  experiments 
should  require  about  25  g.  material,  less  often  50  g.,  which  amount 


FIG.  110. 

may  be  conveniently  handled  in  a  crucible  approximately  5  cm. 
high  and  3  cm.  wide  at  the  top.  The  English  crucibles  made  by 
the  firm  of  Morgan,  Battersea  Works,  London,  are  less  porous, 
extremely  durable,  but  rather  expensive.  Since  these  crucibles 
show  practically  no  tendency  to  absorb  melt,  they  are  to  be 


THERMAL  INVESTIGATION.  299 

especially  recommended  for  work  with  the  more  expensive  metals. 
Graphite  crucibles  may  be  used  to  hold  melts  which  react  strongly 
with  silicates. 

The  crucible  rests  in  a  wire  or  clay  triangle  which  is  surrounded 
by  a  mantle  to  prevent  rapid  heat  radiation  (Fig.  110).  The 
latter  is  about  10  cm.  high  and  consists  of  two  clay  cylinders, 
A  and  B,  of  5  and  8  cm.  diameter,  respectively,  which  are  wrapped 
with  asbestos  and  fitted  together  by  means  of  a  sand  filling.  The 
outside  cylinder  is  bound  with  heavy  iron  wire  suitably  bent  to 
support  the  apparatus  on  an  ordinary  iron  ring  stand  (used  in 
chemical  laboratories).  Some  form  of  bunsen  burner  or  blast 
lamp  is  used  as  a  source  of  heat.  After  removal  of  the  heating 
apparatus,  the  top  opening  of  the  mantle  is  closed  with  an  asbestos 
plate,  and  the  bottom  opening  with  an  iron  saucer  filled  with  sand. 
In  this  way,  rapid  cooling  by  means  of  air  currents  is  avoided. 
To  render  the  cooling  curves  of  various  concentrations  strictly 
comparable,  care  must  be  exercised  that  cooling  invariably  take 
place  under  similar  conditions,  and  that  the  position  of  the  thermo- 
element in  all  melts  be  uniform  as  far  as  is  possible.  The  last 
condition  is  best  guaranteed  by  maintaining  the  protecting 
thermo-element  tube  in  a  vertical  position  touching  the  bottom 
of  the  crucible.  A  small  binding  clamp  attached  to  the  iron 
stand  serves  to  hold  the  tube  in  this  position. 

Melts  which  are  susceptible  to  oxidation  may  often  be  ade- 
quately protected  by  means  of  a  layer  of  ground  charcoal  at  the 
top  of  the  crucible.  A  mixture  of  potassium  chloride  and  sodium 
chloride,  or  of  potassium  chloride  and  magnesium  chloride,  serves 
the  same  purpose.1  Nevertheless  the  best  plan  in  such  cases  is 
to  make  use  of  a  reducing  atmosphere  as  outlined  below  (C). 

B.    For  All  Temperatures. 

The  electric  current  offers  the  best  means  of  obtaining  temper- 
atures above  1100  degrees.  Carbon  resistance  furnaces  heated  by 
means  of  an  alternating  current  of  low  voltage  are  used  at  the 
Goettingen  Laboratory.  Direct  current  at  220  and  440  volts 
enters  the  laboratory,  where  it  is  rendered  suitable  for  heating 
purposes  by  transformation  into  alternating  current  at  5  to  10 

1  ZEMCZUYNYJ,  Z.  anorg.  Chem.,  49,  386  (1906). 


300  THE   ELEMENTS   OF   METALLOGRAPHY. 

volts.  The  first  transformation  is  effected  by  means  of  a  rotary 
transformer,  a  small  model  having  the  capacity  of  about  3  kilo- 
watts, and  furnishing  single-phase  alternating  current  at  150  volts. 
This  current  traverses  the  primary  winding  of  the  second  trans- 
former, which  is  connected  in  series  with  a  rheostat  for  regulation 
purposes.  The  secondary  winding  delivers  300  to  600  amperes  at 
5  to  10  volts.  Copper  bus  bars  carry  the  current  from  the  secon- 
dary transformer  circuit  to  the  furnace.  An  ammeter  indicates 
the  strength  of  current  entering  the  primary  winding,  and  a 
voltmeter  registers  the  voltage  in  the  secondary  circuit.  This 
small  model  is  very  convenient  in  manipulation  for  furnace  work 
requiring  temperatures  in  the  vicinity  of  1500  degrees.  Used  in 
connection  with  the  furnace  of  dimensions  described  below,  there 
is  no  danger  of  fusing  the  porcelain  receptacle  holding  the  melt, 
since,  under  the  most  favorable  conditions,  the  highest  temper- 
ature attainable  can  scarcely  exceed  1600  degrees.  Two  larger 
models  operating  on  the  440-volt  circuit  are  in  use  at  the  Goettin- 
gen  Laboratory.  One  of  these  has  a  maximum  capacity  of  8  kilo- 
watts, the  other  of  10.  Both  deliver  alternating  current  at 
310  volts.  These  machines  are  connected  to  the  alternating 
current  transformer  described  above,  which  furnishes  at  6  to  10 
volts,  in  the  one  case,  current  of  1200  to  700  amperes,  in  the 
other  case  of  1500  to  900  amperes.1 

A  top  view  and  a  vertical  section  of  the  resistance  furnace  are 
shown  in  Fig.  111.  The  resistor  tube  A  is  of  retort  carbon  (from 
Conrady,  Nuremberg)  of  the  following  dimensions:  length,  13  cm., 
inside  diameter,  2  cm.,  outside  diameter,  3  cm.  Two  semicircular 
carbon  plates  B,  2  cm.  in  height  and  9  cm.  in  outside  diameter, 
are  fitted  to  each  end  of  the  tube  A,  and  clamped  securely  by 
means  of  the  bent  copper  bars  C,  2£  cm.  high  and  0.7  cm.  thick, 
which  are  extended  to  a  convenient  length  for  terminal  connections 
with  the  bus  bars.  For  protection  against  rapid  heat  radiation 
from  the  interior  of  the  furnace,  the  clay  cylinder  D  is  clamped 
between  the  carbon  plates  B.  The  space  between  this  clay 
cylinder  and  the  carbon  tube  A  is  filled  with  ignited  charcoal. 
The  furnace  rests  upon  an  iron  saucer  filled  with  sand.  In  setting 

1  The  above  apparatus  was  supplied  by  the  firm  of  Ruhstrat  Brothers, 
Goettingen.  If  alternating  current  is  directly  available,  there  is  obviously  no 
call  for  a  direct  current-alternating  current  transformer. 


THERMAL  INVESTIGATION. 
A 


301 


FIG.  111. 

up  this  apparatus,  a  paste  made  of  tar  and  graphite  powder  is 
used  to  insure  good  conduction  of  the  articulating  parts.  Before 
use,  the  furnace  must  be  gradually  heated  to  expel  volatile  matter. 
When  volatilization  has  ceased  at  1000  degrees,  the  operation  may 
be  considered  complete.  During  use,  the  resistor  tube  A  deterio- 


302  THE   ELEMENTS   OF  METALLOGRAPHY. 

rates  to  such  an  extent  that  it  usually  requires  renewal  after 
some  20  hours'  running.  This  type  of  furnace  may  be  obtained 
from  the  mechanician  of  the  Goettingen  Laboratory,  Ernst  Beulke, 
at  the  price  of  11  marks. 

Porcelain  tubes  of  convenient  dimensions  for  use  in  this  furnace 
are  manufactured  by  the  Royal  Saxon  Porcelain  Manufactory  of 
Meissen.  In  addition  to  those  made  from  the  ordinary  white 
variety  of  porcelain,  others  made  from  a  particularly  refractory 
gray  porcelain  mass  are  used.  If  complete  fusion  of  the  compo- 
nents requires  a  temperature  above  1600  degrees,  at  which  porce- 
lain begins  to  melt,  magnesia  tubes  may  be  substituted.  These 
may  be  obtained  from  the  Royal  Porcelain  Manufactory  of  Berlin. 
They  have  proven  very  satisfactory  in  use,  although  smaller  tubes 
of  this  material  designed  to  protect  the  thermo-element,  have  not, 
thus  far,  fulfilled  the  necessary  condition  of  durability  (in  connec- 
tion with  suitably  thin  wall  substance). 

The  tube  is  allowed  to  project  about  2  cm.  from  the  furnace. 
_^_^_  Fragments  of  arc  lamp  carbons  are  suitable  for  sup- 
porting the  tube  in  this  position.  The  closing  device 
is  of  brass,  bored  in  three  places,  and  generally 
arranged  as  shown  in  cross  section  in  Fig.  112.  The 
length  of  this  metal  cap  is  about  4  cm.,  and  its 
inner  diameter  is  so  chosen  that  it  may  be  fitted  to 
the  tube  at  ordinary  temperature  without  binding. 
The  borings  must  readily  admit  the  porcelain  pro- 
tective tube  for  the  thermo-element.  This  tube 
enters  the  central  opening,  thereby  insuring  a  con- 
sistently central  placement  of  the  element.  The 
second  opening  serves  for  the  introduction  of  a  tube 
carrying  gas,  in  case  experiments  are  conducted  in 
a  nitrogen  (or  other  non-oxidizing)  atmosphere. 
Traces  of  oxygen  are  removed  from  the  ordinary 
nitrogen  which  is  delivered  in  steel  cylinders  under 
pressure  by  passing  it  through  an  alkaline  solution 
of  pyrogallic  acid,  after  which  the  gas  is  dried  by 
•p^Tll2  means  of  sulphuric  acid.  The  third  opening  is  used 
to  admit  a  stirrer,  in  order  that  a  possible  contin- 
gency of  supercooling  may  be  avoided.  Sometimes  it  is  desir- 
able to  use  the  thermo-element  tube  for  this  purpose.  Porcelain 


THERMAL  INVESTIGATION.  303 

tubes  identical  with  those  used  to  protect  the  thermo-element 
are,  in  general,  suitable  for  purposes  of  stirring  and  introducing 
the  neutral  gas. 

If  the  components  possess  very  different  melting  points,  the  most 
difficultly  fusible  one  is  placed  in  the  lower  part  of  the  tube,  since 
a  higher  temperature  is  attained  in  this  region.  The  above 
described  method  of  fusion  is  applicable  to  all  temperatures 
between  some  300  degrees  and  an  upper  limit  approximating 
2000  degrees. 

When  a  considerable  source  of  electrical  energy  at  low  voltage  is 
not  available,  metal  resistance  furnaces  may  be  used.  For  high 
temperatures,  platinum  furnaces  alone  are  suitable.  The  tubes 
used  in  the  construction  of  these  furnaces  are  composed  of  some 
refractory  material  such  as  magnesia,  Marquand  mass,  etc. 
They  are  wound  with  platinum  wire,  or,  according  to  Heraeus, 
best  of  all  with  platinum  foil,  which  carries  the  current  and  must 
accordingly  possess  a  resistance  corresponding  to  the  nature  of 
current  used.  Since  these  refractory  tubes  commence  to  conduct 
electrolytically  at  about  1500  degrees,  and  therefore  bring  about 
gradual  deterioration  of  the  platinum,  furnaces  of  this  type  are 
not  suited  to  continuous  running  above  this  temperature.  Aside 
from  this  disadvantage,  they  are  generally  inferior  to  carbon 
resistance  furnaces:  e.  g.,  they  require  very  carefully  handling 
and  it  is  difficult  to  repair  them. 


C.    For  Temperatures  up  to  800  Degrees  and  1100  Degrees, 
Respectively,  in  a  Protective  Atmosphere. 

If  fusion  is  to  be  effected  in  a  protective  atmosphere,  it  is  desir- 
able to  reject  the  use  of  crucibles,  even  when  heating  is  other  than 
electrical  in  nature,  and  to  make  use  of  an  arrangement  sketched 
in  Fig.  112,  wherein  tubes  of  porcelain,  or  of  other  material,  are 
substituted.  The  mantel  shown  in  Fig.  110  is  desirable  in  this 
case,  provided  temperatures  up  to  1100  degrees  must  be  attained. 
For  temperatures  not  exceeding  800  degrees,  tubes  of  difficultly 
fusible  glass,  e.  g.,  of  Jena  combustion  tubing,  are  excellent,  if  not 
attacked  by  the  melt.  The  admirable  arrangement  used  by  GRUBE* 

1  GRUBE,  Z.  anorg.  Chem.,  44,  117  (1905). 


304 


THE  ELEMENTS  OF  METALLOGRAPHY. 


in  investigating  magnesium  alloys,  is  shown  in  Fig.  113.  The 
glass  melting  tube  A  is  contained  in  a  cylindrical  iron  sand  bath 
B,  which  is  heated  by  means  of  a  powerful  combination  of  four 
burners,  thus  avoiding  local  overheating.  The  sand  bath  is  sur- 
rounded by  an  asbestos  mantle  C,  which  is  closed  above  by  a  mat 
of  the  same  material,  and  also  below,  during  cooling,  by  a  shallow 
iron  dish  filled  with  sand.  The  glass  tube  is  fitted  with  a  cap  D, 
similar  to  that  pictured  on  p.  302.  Through 
the  three  openings  in  this  cap,  a  stirrer  F,  gas 
leading  in  tube  G,  and  a  glass  protective  tube 
E  E,  enclosing  the  thermo-element,  are  intro- 

duced. Grube  used  an  atmosphere  of  hydro- 
gen, which  was  found  to  operate  at  800 
degrees  without  injury  to  the  thermo-element 
(cf.  p.  297). 


FIG.  113. 


§  3.  THE  DETERMINATION  OF  COOLING 
CURVES,  AND  HEATING  CURVES,  RE- 
SPECTIVELY. 

In  opening  the  investigation  of  a  binary 
alloy,  it  is  desirable,  for  the  purpose  of  obtain- 
ing a  general  survey,  that  the  determination 
of  cooling  curves  proceed  regularly  (from 
concentration  to  concentration),  throughout  the  whole  concen- 
tration range,  at  intervals  of  10  per  cent.1  The  amount  of 
material  necessary  for  an  individual  determination  may  vary 
from  20-30  g.,  according  to  the  specific  weight  of  the  metals  in 
question.  The  metals  are  heated  until  completely  melted,  and 
stirred  until  a  uniform  mixture  is  attained.  Immediately  after 
direct  heating  has  been  discontinued,  some  further  elevation 
in  temperature  is  observed.  This  is  due  to  a  certain  delay 
attending  transfer  of  heat  from  the  walls  of  the  vessel  to 
the  thermo-element.  Furthermore,  this  condition  causes  a 
rate  of  cooling  which  is  less  than  normal  to  ensue  directly  after 
the  temperature  has  reached  a  maximum  and  has  started  to 

1  Concerning  the  logical  choice  of  concentrations  in  the  investigation  of  a 
three  component  system,  compare  SAHMEN  and  VEGESACK,  Z.  anorg.  Chem., 
59,  262  (1907). 


THERMAL  INVESTIGATION.  305 

fall.  On  this  account,  it  is  desirable,  if  possible,  to  heat  the 
mixture  some  50  degrees  above  the  temperature  at  which  primary 
observation  is  to  be  made.  In  determining  a  cooling  curve,  the 
temperature  of  the  cooling  melt  is  noted  at  regular  intervals, 
usually  from  10  to  10  seconds,  sometimes  from  5  to  5  seconds  as 
indicated  by  a  suitable  (stop)  watch,  and  this  collection  of  tem- 
perature observations  is  plotted  against  the  time,  as  described  on 
page  4.1 

Melts  frequently  tend  to  supercool.  This  condition  is  rendered 
evident  in  most  cases  by  the  appearance  of  a  sudden  elevation  in 
temperature  when  the  melt  finally  begins  to  crystallize.  If  we  are 
dealing  with  solidification  of  a  mixture,  this  elevation  will  in  no 
case  reach  the  temperature  at  which  normal  crystallization  of  one 
variety  occurs.  Therefore,  we  always  seek  to  eliminate  supercool- 
ing. This  may  usually  be  effected  by  thorough  stirring.  When 
stirring  fails  to  establish  normal  conditions,  it  is  necessary  to 
inoculate  the  melt  with  a  particle  of  solid  material  obtained  from 
a  previously  cooled  melt.  Introduction  of  the  solid  material 
should  be  opportune,  i.  e.,  it  should  take  place  at  a  moment 
(ascertained  by  preliminary  experiment)  when  the  temperature 
of  the  melt  is  only  a  few  degrees  above  the  value  which  normally 
determines  crystallization,  and  it  should  be  accompanied  by  vigor- 
ous stirring. 

Determination  of  a  heating  curve,  following  that  of  the  cooling 
curve,  is  most  advisable,  since  it  offers  a  most  reliable  check  on 
the  latter  data.  Addition  of  heat  must  obviously  be  made  with 
the  greatest  possible  uniformity;  a  result  easily  attained  by  the 
aid  of  electrical  apparatus.  Pure  metals  and  their  pure  com- 
pounds are  not  subject  to  superheating.  But  superheating  may 
well  be  encountered  in  the  case  of  mixtures,  since  here  the  melt- 
ing point  of  one  component  is  not  reached  at  the  time  of  fusion, 
and  we  are  obviously  dealing  with  a  solution  process.  Neverthe- 
less, resulting  complications  are  not,  as  a  rule,  prevalent.  Par- 
ticularly when  supercooling  occurs  in  a  melt  which  is  already 
partially  solidified  and  is  consequently  not  amenable  to  stirring 
or  to  inoculation,  determination  of  heating  curves  is  frequently 
our  only  means  of  explaining  the  crystallization  processes. 

1  Another  graphical  method  consists  in  representing  the  rate  of  cooling,  or 
its  reciprocal  value,  as  a  function  of  the  temperature. 


306  THE  ELEMENTS   OF   METALLOGRAPHY. 

Self-registering  pyrometers  which  are  based  upon  the  use  of 
mirror  galvanometers  and  photographically  depict  the  deflection 
of  the  galvanometer  needle  as  a  function  of  the  time,  have  been 
described  by  ROBERTS- AUSTIN/  SALADIN  and  LECH  ATELIER/ 
and  KuRNAKOW.3  A  self-registering  instrument  without  mirror 
suspension  is  manufactured  by  the  firm  of  Siemens  and  Halske.4 

§4.     CONSTRUCTION  OF  IDEALIZED  COOLING  CURVES  AND 
HEATING  CURVES,  RESPECTIVELY. 

The  form  of  an  experimentally  determined  cooling  curve 
differs  in  many  respects  from  that  developed  in  our  theoretical 
discussion.  This  is  due  to  the  fact  that  certain  assumptions 
which  we  made  relative  to  the  behavior  of  substances  in  general 
and  to  the  method  of  experimentation  are  never  completely 
(often,  indeed,  most  incompletely)  realized.  Since  we  are,  as  a 
rule,  fully  cognizant  of  the  reasons  underlying  such  deviation,  it 
is  not  difficult  to  construct  altered  or  "idealized"  curves,  based 
upon  the  actual  curves,  which  shall  closely  correspond  to  a  full 
realization  of  our  preliminary  hypotheses.  The  cooling  curve 
of  a  pure  substance  (silver)  is  given  in  Fig.  114,  I,  as  determined 
with  the  aid  of  a  carbon  resistance  furnace.  Divisions  on  the  time 
axis  correspond  to  100  seconds,  those  on  the  temperature  axis  to 
100  degrees.  Since  no  supercooling  has  resulted,  the  beginning 
of  crystallization  is  sharply  indicated  on  the  curve.  No  equally 
marked  change  in  direction  of  the  curve  shows  the  time  at  which 
crystallization  has  ceased ;  on  the  contrary,  the  temperature  began 
at  the  point  /  to  fall  slowly,  thereupon  falling  more  and  more 
rapidly  as  far  as  the  point  c,  which  constitutes  a  point  of  inflec- 
tion, and  finally  falling  off  at  a  constantly  decreasing  rate,  as 
shown  by  the  portion  cde.  The  reason  for  this  phenomenon, 
which  is  associated  with  all  experimental  cooling  curves,  is  defined 
by  TAMMANNS  as  follows:  Flow  of  heat  takes  place  not  only  from 
the  surface  of  the  melt  outwards,  but  also  through  the  thermo- 

1  ROBERTS-AUSTIN,  Five  notes  to  the  Institute  of  Mechanical  Engineers, 
Proceedings,  93,  95,  97,  99  (1891). 

2  SALADIN  and  LECHATELIER,  Revue  de  metallurgie,  February  (1904). 

3  KURNAKOW,  Z.  anorg.  Chem.,  42,  184  (1904). 

4  Zeitschr.  f.  Instrumentenkunde,  25,  273  (1905). 
6  TAMMANN,  Z.  anorg.  Chem..  47,  291  (1905). 


THERMAL   INVESTIGATION. 


307 


metric  apparatus.  Furthermore,  the  previously  assumed  good 
heat  conductivity  (cf.  p.  17),  which  would  preclude  the  existence 
of  measurable  temperature  differences  within  the  system,  is  not 

Temperature 


c*  .* 


FIG.  114. 

completely  realized.  When  a  melt  in  the  crucible  A  (Fig.  115), 
containing  a  centrally  located  thermometer  B,  cools  off,  a  crust 
of  crystals  is  deposited,  not  only  on  the  crucible  walls,  but  also 
around  the  thermometer.  The  final  remainder  of  the  melt  there- 


308  THE  ELEMENTS   OF   METALLOGRAPHY. 

fore  crystallizes  in  the  space  CCC,  the  distance  of  which  from  the 
thermometer  B  will  become  less,  in  proportion  as  the  relation 
between  the  heat  quantity  passing  away  through  the  thermom- 
eter to  that  flowing  through  the  crucible  walls  diminishes.     We 
see  that  a  difference  between  the  temperature  of 
the  thermometer  and  that  of  the  melt  will  result 
if  the  quantity  of  heat  flowing  toward  the  ther- 
mometer is  smaller  than  that  which  the  thermom- 
eter conducts  away.     This  condition  of  affairs  is 
observed  from  the  point/  onwards  (Fig.  114,  1) 
—  a   gradual  falling  of  the  measured  tempera- 
ture occurs,  although  the  remainder  of  the  melt 
crystallizes     at     constant     temperature.     Since 
FIG.  115.         heat   flow  toward  the  thermometer  is  rendered 
increasingly  difficult  by  reason  of  the  continually 
increasing  thickness  of  the  crystalline  crust,  the  rate  of  cooling 
becomes  more  rapid  and  reaches  a  maximum  at  the  point  c, 
where  we  must  regard  crystallization  as  complete.     Henceforth, 
cooling  becomes  more  gradual,  and  rapidly  attains  a  normal  value, 
which  does  not  vary  greatly  within  a  moderately  limited  tem- 
perature range. 

The  fact  that  from  the  time  when  no  further  heat  of  crystalli- 
zation is  transferred  to  the  thermometer  an  unusually  rapid 
temperature  decrease  ensues,  finds  its  explanation  in  the  absolute 
non-fulfillment  of  another  of  our  primary  assumptions  (cf.  p.  17), 
namely,  that  the  cooling  takes  place  against  surroundings  which 
preserve  constant  temperature  (constant  convergence  tempera- 
ture). The  melt  is  placed,  at  the  outset,  in  a  vessel,  the  mass 
of  which  cannot  be  neglected  in  comparison  with  that  of  the  melt. 
Since  we  are  investigating  the  cooling  of  the  melt  alone,  we  must 
regard  the  containing  vessel,  in  so  far  as  its  temperature  differs 
from  that  of  the  melt,  as  part  of  the  surroundings.  This  vessel 
is  again  surrounded  by  a  heat  retainer,  i.e.,  the  hot  carbon  tube  of 
the  furnace  with  its  own  further  heat  insulation,  or  a  clay  mantle, 
etc.  These  surroundings  also  gradually  cool  off.  Thus,  the  melt 
cools  in  the  presence  of  surround  ngs  which  themselves  possess 
variable,  gradually  decreasing  temperature.  In  general,  no  par- 
ticularly obvious  deviation  from  the  theoretical  form  of  cooling 
curve,  such  as  might  result  from  these  modifying  influences,  is 


THERMAL  INVESTIGATION.  309 

actually  observed:  the  experimental  curves  actually  show  the 
logarithmic  form  (or  a  very  similar  form)  developed  on  page  12 
et  seq.,  and  illustrated  in  Fig.  3  (p.  14).  We  obtain  a  quite  differ- 
ent result,  however,  when  the  melt  is  maintained  at  constant 
temperature  for  a  certain  length  of  time  through  the  agency  of  an 
internal  source  of  heat.  During  this  time,  the  immediate  sur- 
roundings cool  off  unhampered,  the  temperature  difference  be- 
tween them  and  the  melt  increasing  until  a  maximum  difference 
is  reached  at  the  moment  the  above-mentioned  heat  source  be- 
comes exhausted  (when  crystallization  of  the  melt  is  completed). 
An  increased  rate  of  cooling  will  be  indicated  by  the  thermo- 
element until  this  temperature  difference  has  again  reached  the 
normal  value.  Conditions  of  this  sort  are  observed  at  the  points 
c  and  d  (Fig.  114,  I). 

Now,  in  order  to  deduce  the  approximately  theoretical  form 
of  cooling  curve,  let  us  reflect  that  the  portions  ab  and  de  of  the 
experimentally  determined  curve  (Fig.  114,  I)  are  themselves 
sufficiently  accurate  to  stand.  By  prolonging  the  portion  de 
continuously  over  d  as  far  as  the  point  of  intersection  g  with 
the  horizontal  drawn  through  b,  we  construct  an  idealized  cool- 
ing curve  abgde,  which  coincides  above  b  and  below  d  with  the 
experimental  curve. 

Fig.  114,  II,  gives  a  heating  curve  of  the  same  material  (pure 
silver).  This  was  also  obtained  with  the  aid  of  the  electric 
furnace.  Here,  fusion  commenced  at  the  walls  of  the  vessel, 
and,  consequently,  flow  of  heat  toward  the  thermo-element  was 
most  hindered  in  the  beginning,  becoming  more  perfect  as  the 
crystalline  layer  melted  away  from  the  thermo-element.  In 
accordance  with  the  conditions  just  noted,  there  is  no  constant 
temperature  to  be  observed  on  the  heating  curve,  corresponding 
to  the  beginning  of  fusion,  but  rather  a  very  gradual  rise  in  tem- 
perature. When  all  of  the  alloy  has  melted,  an  abrupt  change 
in  the  rate  of  temperature  increase  is  observed  —  the  tempera- 
ture begins  to  rise  at  a  rapid  rate,  whence  a  change  in  the  direc- 
tion of  the  curve  ensues  at  this  point.  The  construction  of  an 
idealized  heating  curve  may  be  carrljd  out  as  described  above 
relative  to  the  cooling  curve. 

Fig.  114,  III  gives  the  cooling  curve  of  pure  palladium. 
Supercooling  has  taken  place  in  this  case. 


310  THE  ELEMENTS   OF   METALLOGRAPHY. 

Fig.  114,  IV  gives  the  cooling  curve  of  an  alloy  composed  of 
70%  Pd  and  30%  Pb.  First,  a  single  crystalline  variety  sepa- 
rates for  a  time,  beginning  at  a.  Then,  from  b  onwards,  eutectic 
crystallization  follows.  In  all  of  these  cases,  " idealized"  curves 
may  be  derived  from  the  experimental  curves. 

We  have  seen  in  the  theoretical  part  of  this  book  how  import- 
ant knowledge  of  the  relative  amounts  of  eutectic  at  various 
concentrations  is  with  respect  to  determination  of  the  consti- 
tution of  the  alloy.  Now,  the  heat  quantity  liberated  during 
crystallization  of  the  eutectic  is  proportional  to  the  amount  of 
eutectic  present.  Thus,  on  comparing  equal  weights  of  alloys 
of  different  concentrations,  these  heat  quantities  are  propor- 
tional to  the  relative  amounts  of  eutectic  in  the  several  cases. 
If  cooling  were  to  occur  in  an  ideal  manner  (according  to  the 
description  beginning  on  p.  17),  then,  under  similar  conditions 
and  for  the  same  quantities  of  melt  of  different  concentrations, 
the  periods  of  eutectic  crystallization  would  be  proportional  to 
the  heat  quantities  liberated  and  consequently  to  the  relative 
amounts  of  eutectic  in  the  different  alloys.  We  would,  there- 
fore, possess  in  this  method  of  procedure  a  means  for  deter- 
mination of  the  relative  amounts  of  eutectic.  Since,  when  the 
concentration  axis  is  made  to  show  weight  per  cent  (see  p.  107) 
the  relative  amounts  of  eutectic  decrease  lineally  from  their 
maximum  of  1  towards  both  zero  points,  a  linear  decrease  would 
be  expected  relative  to  the  duration  of  eutectic  crystallization. 

Experience  fails  to  completely  substantiate  this  conclusion, 
as  we  have  seen.  We  find  in  addition  to  a  linear  decrease  in 
eutectic  periods,  as  represented  in  Fig.  116  (shown  by  verticals 
drawn  in  proportion  to  the  periods  of  eutectic  crystallization  in 
the  various  concentrations),  a  too  gradual  decrease  (Fig.  116,  II), 
and  a  too  rapid  decrease  (Fig.  116,  III).  Too  gradual  decrease 
may  be  readily  explained  on  the  basis  of  our  experimental  con- 
ditions. We  have  seen  that  while  the  temperature  of  the  melt  is 
kept  constant  by  the  influx  of  heat  of  crystallization,  the  material 
adjacent  to  the  melt  continues  to  cool  down.  Since  the  heat 
quantity  dissipated  in  a  unit  time,  ceteris  paribus,  is  propor- 
tional to  the  temperature  difference  between  melt  and  adjacent 
material,  it  follows  that  the  heat  quantity  necessary  to  maintain 
constant  temperature  is  greater  in  proportion  as  this  period 


THERMAL  INVESTIGATION. 


311 


lengthens.  On  this  account,  when  the  amount  of  eutectic  is 
doubled,  the  corresponding  eutectic  period  (of  constant  tem- 
perature), will  be  less  than  twice  that  before. 

The  frequently  observed  too  rapid  decrease  (Fig.  116,  III),  is 
probably  due  to  a  tendency  of  the  substance  towards  supercool- 
ing. When  a  large  amount  of  eutectic  is  present,  and  separation 
of  two  crystalline  varieties  has  begun  at  any  one  point,  a  large 


3 


I^r 


11 


771 


Weight  per  cent  B 
FIG.  116. 


100 


number  of  crystalline  particles  may  be  regularly  disposed 
throughout  the  main  quantity  of  melt  by  stirring,  whereby 
orderly  crystallization,  regulated  alone  by  the  flow  of  heat 
throughout  the  material,  may  ensue.  Quite  different  results  are 
to  be  expected  when  the  amount  of  eutectic  is  small,  and  that 
which  still  remains  molten  towards  the  end  of  crystallization  is 
situated  in  different  parts  of  the  mixture  between  masses  of  crys- 


312  THE   ELEMENTS   OF   METALLOGRAPHY. 

talline  material  (too  much  solid  material  being  present  to  admit 
of  stirring).  In  such  a  case,  separation  of  eutectic  in  these  differ- 
ent localities  may  take  place  at  unequally  retarded  rates,  and 
the  temperature,  instead  of  remaining  constant  during  crystal- 
lization, may  vary  more  or  less.  It  is  possible  that  the  resulting 
change  in  the  course  of  the  cooling  curve  may  be  sufficiently 
slight  to  escape  observation  when  the  experimental  results  are 
plotted.  Thus,  a  too  rapid  decrease  in  the  eutectic  period  (with 
the  concentration)  is  characteristic  of  the  case  just  discussed, 
whereby  eutectic  crystallization,  may  apparently  cease  before 
the  amount  of  eutectic  has  actually  become  0. 

By  compensating  both  disturbing  influences  noted  above,  it  is 
often  possible  to  obtain  the  theoretical  (linear)  relation  between 
eutectic  time  intervals  and  concentration.  Experience  has 
shown  that,  in  general,  even  when  such  compensations  are  not 
made,  the  concentrations  which  are  of  most  vital  interest 
namely,  those  at  which  the  relative  amounts  of  eutectic  reach 
their  maxima  or  minima  respectively,  are  susceptible  to  rather 
accurate  experimental  determination.  To  ascertain  such  con- 
centrations, a  curve  joining  the  end  points  of  the  verticals  (pro- 
portional to  the  eutectic  periods),  is  continued  up  to  its  points  of 
intersection  with  the  base  upon  which  they  are  erected.  These 
points  of  intersection  correspond  to  the  concentrations  sought. 

In  order  to  realize  uniform  cooling  conditions,  it  is  obviously 
necessary  that  the  receptacles  used  to  hold  the  various  melts  in 
the  series  be  closely  similar;  that  the  heat  insulation  be  com- 
parable in  all  cases,  etc.  Moreover,  it  is  necessary  to  use  ap- 
proximately the  same  volume  of  melt  in  the  several  instances. 
If  the  densities  of  the  two  components  are  very  different,  reali- 
zation of  the  latter  condition  implies  the  use  of  widely  varying 
weights  of  material  in  the  different  concentrations.  In  such 
cases,  the  observed  eutectic  periods  of  crystallization  must  be 
divided  by  the  weights  of  the  corresponding  melts,  in  order  that 
numbers  which  shall  apply  to  a  definite  weight  of  melt  may  be 
obtained.  Since,  according  to  equation  4,  p.  15,  the  product  of 
rate  of  cooling  and  specific  heat  is  constant  under  the  same  con- 
ditions of  cooling,  a  uniform  rate  of  cooling  in  the  various  melts 
is  to  be  expected  only  when  the  specific  heat  does  not  vary  with 
the  concentration. 


THERMAL  INVESTIGATION.  313 

When  the  components  form  mixed  crystals  with  one  another, 
the  temperature  at  which  crystallization  ceases  is  usually  very 
imperfectly  indicated  on  the  cooling  curves.  This  is  illustrated 
in  Fig.  114,  V.  The  cooling  curve  refers  to  a  mixture  of  90  per 
cent  silver  and  10  per  cent  palladium.  Only  the  beginning  of 
crystallization  is  quite  apparent  (at  b)  on  examining  the  curve. 
The  point  of  inflection  c  is  used,  according  to  the  procedure  of 
Tammann,  in  ascertaining  the  end  of  crystallization.  At  this 
point,  the  rate  of  cooling  is  most  rapid,  and  crystallization  is 
to  be  regarded  as  complete.  It  would,  however,  be  incorrect  to 
consider  the  whole  temperature  interval  be  as  the  crystallization 
interval  710%  Pd.  For,  on  this  basis,  a  similar  crystallization 
interval  be  (Fig.  114,  I)  would  of  necessity  pertain  to  pure  silver, 
which  must  crystallize  at  constant  temperature.  Therefore,  a 
certain  quantity  A7,  which  could  be  obtained  by  determining 
the  apparent  crystallization  interval  corresponding  to  crystalliza- 
tion of  a  pure  substance  at  the  same  temperature  under  the  same 
cooling  conditions,  must  be  deducted  from  the  apparent  crystalli- 
zation interval  710%  Pd  to  render  the  latter  correct. 

Tammann  uses  an  indirect  method  wherein  calculation  of  the 
quantity  A7  is  made  from  the  apparent  crystallization  intervals 
of  both  components  by  applying  the  rule  of  mixture.  If  7A  and 
7B  are  the  apparent  crystallization  intervals  for  the  components 
A  and  B,  respectively,  and  if  the  corresponding  concentration  in 
weight  per  cent  B  is  x  —  whence  the  alloy  contains  x%  B  and 
(100  —  x)%  A  —  then  the  quantity, 


must  be  deducted  from  the  apparent  crystallization  interval  7. 

In  many  cases,  the  crystallization  interval  may  be  recognized 
at  once  upon  the  heating  curve.  Thus,  Fig.  114,  VI,  shows  the 
heating  curve  for  the  same  mixture,  90  per  cent  Ag  +  10  per 
cent  Pd,  for  which  Fig.  114,  V,  gives  the  cooling  curve.  The 
beginning  of  fusion,  at  the  point  c,  where,  owing  to  very  gradual 
heating,  a  rather  marked  deviation  of  the  heating  curve  from  its 
previously  linear  course  occurs,  is  here  very  clear,  although  not 
so  sharply  marked  as  the  end  of  fusion  at  b.  The  value  to  be  de- 
ducted in  this  case  for  the  apparent  interval  of  a  pure  substance 


314  THE  ELEMENTS   OF   METALLOGRAPHY. 

is  comparatively  small,  as  is  evident  on  comparison  of  the  curves, 
Fig.  114,  I  and  II,  and  may  be  regarded  as  constant  (to  within 
5  degrees  under  present  conditions). 

If  the  crystallization  interval  is  very  small,  the  following  pro- 
cedure may  be  suggested  for  determining  it.1  In  normal  cases, 
i.e.,  when  an  excessive  quantity  of  heat  is  not  conducted  away 
by  the  thermometer,  the  point/  (Fig.  114,  I)  at  which  the  ther- 
mometer begins  to  register  a  fall  of  temperature  during  crystalli- 
zation of  a  pure  substance  lies  in  the  last  third  of  the  period  of 
crystallization.  Therefore,  if  the  point  6,  which  indicates  the 
beginning  of  crystallization,  is  joined  to  the  point  /,  which  corre- 
sponds to  some  two-thirds  of  the  period  of  crystallization,  a 
straight  line  is  obtained  in  the  case  of  a  pure  substance.  If, 
however,  we  are  dealing  with  mixed  crystals  (Fig.  114,  VII), 
bf  is  inclined  to  the  time  axis.  An  extension  of  the  straight  line 
bf  to  the  point  h,  which  corresponds  to  the  end  of  crystallization, 
then  yields  the  required  crystallization  interval  hi. 

We  see  from  the  above  that  the  determination  of  a  crystalli- 
zation interval  through  the  agency  of  cooling  curves  is  compar- 
atively uncertain  in  the  case  of  mixed  crystals,  the  difficulty 
pertaining  to  location  of  the  end  point  of  crystallization.  At 
this  juncture,  we  may  cite  the  method  of  HEYCOCK  and  NEVILLE, 2 
according  to  which,  in  their  investigation  of  copper-tin  alloys 
(bronzes),  the  end  points  of  crystallization  were  ascertained  by 
quenching  the  alloys  at  various  temperatures,  and  subjecting 
polished  sections  of  the  resulting  material  to  microscopical  exam- 
ination. The  separating  crystals  are  larger  in  proportion  to  the 
slowness  with  which  they  crystallize.  Hence,  those  crystals  which 
have  separated  before  quenching  are  readily  distinguished  by 
reason  of  their  larger  size  from  those  which  have  formed  after 
quenching.  If  small  crystals  are  entirely  absent  in  the  section, 
quenching  has  occurred  after  all  the  material  has  crystallized. 
In  this  manner,  it  is  possible  to  determine  the  end  points  of 
crystallization  in  the  several  concentrations  with  considerable 
accuracy.  Such  accurate  determination  of  the  crystallization 
interval  is  obviously  of  value  only  when  it  is  certain  that  the  con- 
centration balance  (see  p.  173)  necessary  for  realization  of  equilib- 

1  RUER,  Z.  anorg.  Chem.,  49,  379  (1906). 

2  HEYCOCK  and  NEVILLE,  Phil.  Trans.,  202.  1  (1903). 


THERMAL   INVESTIGATION.  315 

rium  has  reached  a  degree  approximating  perfection,  since,  in 
such  cases  alone,  does  the  curve  joining  the  final  temperatures  of 
crystallization  coincide  with  the  s-curve.  Finally,  it  may  be  stated 
that  a  faint  break  in  the  cooling  curve  appears  most  plainly 
when  the  latter  is  drawn  so  as  to  incline  about  45  degrees  toward 
the  axes.1 

1  BOEKE,  Z,  anorg.  Chem.,  50,  358  (1906). 


CHAPTER    II. 
INVESTIGATION  OF  STRUCTURE. 

CONTINUED  reference  to  the  importance  of  microscopical  inves- 
tigation of  polished  sections  for  the  purpose  of  regulating  and 
supplementing  the  results  of  thermal  investigation  has  been  made 
in  the  theoretical  part  of  this  text.  The  task  of  harmonizing  the 
results  of  both  methods  of  investigation  proves  in  many  cases 
extremely  difficult,  and  severely  taxes  the  experience  of  workers 
in  the  metallographical  field.  Particularly  when  the  existence  of 
mixed  crystals  is  indicated  by  thermal  investigation  are  we  likely 
to  obtain  results  on  microscopical  examination  which  are  more 
or  less  at  variance  with  those  to  be  expected.  We  have  already 
noted  (on  p.  180)  how  it  may  be  shown  in  such  cases  that  inhomo- 
geneous  structure  of  reguli  finds  its  explanation  purely  in  incom- 
plete concentration  balance  between  crystals  and  melt  during 
solidification.  In  the  main,  we  are  indebted  to  SORBY,  MARTENS, 
HEYN,  BEHRENS/  OSMOND,'  WEDDING,  and  LECHATELIERS  for 
the  development  of  microscopical  methods  of  investigation. 

§1.    PREPARATION  OF  SECTIONS. 

To  serve  the  purposes  of  microscopical  investigation,  a  chosen 
section  of  the  cold  regulus  is  usually  brought  to  a  mirror-like 
surface,  several  square  centimeters  in  area,  by  cutting  and  polish- 
ing. The  manner  of  obtaining  this  result  varies  according  to  the 
properties,  in  particular,  the  hardness,  of  the  alloy  in  question. 
In  case  of  a  soft  alloy,  it  may  be  unusually  difficult,  or  indeed 

1  BEHRENS,   Das  mikroscopische  Gefiige  der  Metalle  und  Legierungen, 
Hamburg  and  Leipzig,  1894. 

2  OSMOND,  Methode  ge'ne'rale  pour  Tanalyse  micrographique  des  aciers  au 
carbone.     Contribution  a  l'e"tude  des  alliages,  Paris,  1901,  p.  277.     German 
translation  of  the  same  by  L.  Heurich,  under  the  title,  Mikrographische 
Analyse  der  Eisen-Kohlenstofflegierungen,  Halle,  1906. 

3  LECHATELIER,  Contribution  a  l'e"tude  des  alliages,  p.  421. 

316 


INVESTIGATION   OF  STRUCTURES.  317 

impossible,  to  obtain  a  surface  which  will  show  no  polishing 
scratches  under  the  microscope.  Since  we  are  in  a  position,  after 
some  practice,  to  distinguish  such  scratches  from  striations  which 
may  be  characteristic  of  the  structure  of  the  crystals  themselves, 
the  above  limitation  does  not  constitute  an  absolute  hindrance 
to  the  progress  of  microscopical  work. 

It  is,  nevertheless,  of  great  importance  that  the  composition  of 
the  alloy  in  its  different  parts  be  uniform.  If  the  crystals  which 
first  separate  are  widely  different  from  the  mother  liquor,  as 
regards  specific  weight,  they  readily  collect  in  the  upper  or  lower 
part  of  the  melt  and  are  thus  open  to  dissimilarity  in  their  general 
make-up.  Microscopical  investigation  may  then  easily  lead  to 
false  conclusions.  Frequently,  the  external  appearance  of  the 
section  alone  indicates  that  the  upper  and  lower  parts  have  been 
formed  under  unlike  conditions,  as  above.  In  other  cases,  micro- 
scopical examination  of  a  longitudinally  cut  section  must  be 
undertaken  in  order  to  determine  whether  or  not  this  effect 
has  occurred.  If  evidence  of  a  tendency  toward  " segregation," 
as  such  phenomena  are  named,  has  accrued,  too  slow  cooling  of 
the  melt  should  be  avoided  and  the  additional  safeguard  of  vigor- 
ous stirring  should  be  brought  into  requisition.1 

If  the  regulus  under  investigation  is  hard  (hardness  4  and  over) , 
and  is  composed  of  material  of  a  sufficiently  cheap  variety,  it  may 
best  be  brought  to  a  smooth  surface  by  grinding  on  emery  or 
carborundum  wheels.  In  this  operation,  the  sample  is  passed 
from  the  coarser  to  the  finer  wheels  by  degrees.  At  the  Goettin- 
gen  Institute,  a  small  electric  motor  running  at  about  1800  revo- 
lutions per  minute  is  used  as  a  polishing  machine  by  attaching 
the  polishing  plates  directly  to  its  revolving  (horizontal)  axis. 
Obviously,  hand  polishing  stones  may  be  used  as  well.  Care 
should  be  taken  that  the  reguli  do  not  become  hot  during  their 
manipulation,  since  this  may  bring  about  changes  in  structure. 
To  avoid  any  such  possibility,  they  may  be  dipped  into  water 
from  time  to  time  during  the  course  of  the  grinding  and  pol- 
ishing. Further  treatment  of  the  sections  is  carried  out  with 
graded  sizes  of  emery  cloth.  Osmond  (1.  c.)  requires  the  follow- 
ing of  an  emery  cloth:  the  grain  must  be  uniform;  the  emery 
powder  must  adhere  to  the  backing  so  firmly  that  it  does  not 

1  Compare,  also,  p.  138  and  following  pages. 


318  THE  ELEMENTS   OF   METALLOGRAPHY. 

become  detached  on  rubbing;  the  powder  must  wear  away  in 
streaks  but  not  in  spots,  as  is  the  case  when  it  adheres  loosely; 
finally,  the  cloth  (or  paper)  and  the  glue  themselves  must  not 
score  soft  iron.  Since  the  commercial  article  satisfies  these 
demands  only  infrequently,  he  adds  directions  relative  to  the 
preparation  of  satisfactory  emery  cloth,  and  concerning  which 
the  reader  is  referred  to  the  original.  The  so-called  French  emery 
paper,  manufactured  by  the  firm  of  Georg  Voss  &  Co.,  Deuben, 
Dresden,  Germany,  is  used  at  the  Goettingen  Institute.  This  is 
prepared  in  the  grainings,  3,  2,  1,  0,  00  minutes,  and,  further- 
more, 0,  1,  2,  3,  5,  10,  15,  20,  30  and  60  minutes.  In  general,  six 
varieties,  e.g.,  3,  1,  and  10,  20,  30  and  60  minutes,  will  be  found 
adequate. 

The  emery  cloth  is  tacked  on  right  angled  wooden  blocks 
(about  30  X  15  cm.),  upon  which  the  section  is  then  rubbed  back 
and  forth.  Polishing  on  each  separate  number  of  emery  cloth 
should  be  so  carried  out  that  the  lines  of  abrasion  run  in  a  definite 
direction.  On  passing  to  another  number,  the  operation  is  con- 
tinued in  a  direction  at  right  angles  to  these  lines,  until  the  latter 
are  completely  obliterated,  i.e.,  replaced  by  a  new  series.  Thus, 
it  develops  that  the  scratches  from  the  last  number  of  emery  cloth, 
even  though  they  may  fail  to  disappear  completely  on  subsequent 
polishing,  are,  nevertheless,  hardly  distinguishable  as  such,  since 
they  preserve  the  same  direction  over  the  whole  surface.  Such 
direction  is  indeed  likely  to  be  that  corresponding  to  the  general 
disposition  of  the  crystal  polygons.  Finally,  polishing  is  finished 
most  effectually  with  a  revolving  felt  or  leather  disc  bearing 
metal-polishing  wax  upon  its  surface.  In  case  use  is  made  of 
a  wax  preparation  in  grinding  the  regulus,  great  care  should  be 
taken  that  none  of  this  reaches  the  polishing  disc,  since  the  latter 
may  be  ruined  in  this  way  for  polishing  purposes. 

The  reguli  of  especially  brittle  alloys  may  be  broken  into  pieces 
from  which  selection  of  those  showing  smooth  surfaces  may  be 
made  with  a  view  to  further  mechanical  treatment. 

Emery  or  carborundum  wheels  should  not  be  used  on  soft 
alloys,  in  order  that  serious  contamination  of  the  latter  with 
foreign  metallic  particles  be  avoided.  Coarse  and  fine  files  in 
succession  are  best  used  in  working  such  material  into  shape. 
Further  treatment  with  emery  cloth  follows  in  the  manner  de- 


INVESTIGATION  OF  STRUCTURES.  319 

scribed  above.  Eventually,  they  are  polished  on  a  piece  of 
felt  or  soft  leather  which  is  stretched  over  a  smooth  block  and 
used  in  connection  with  Vienna  chalk  and  polishing  oil  (stearin 
oil).  According  to  Behrens  (1.  c.),  certain  alloys  which  are  trouble- 
some by  reason  of  their  softness  and  friability  assume  an  excellent 
polish  when  rubbed  on  fine  whetstones  moistened  with  a  trace  of 
kerosene  —  a  drop  of  kerosene  is  rubbed  into  the  stone  with  the 
finger,  vigorously  wiped  with  a  cloth  and  rubbed  with  the  ball  of 
the  hand  until  the  stone  appears  quite  dry.  Osmond  uses  English 
red  —  the  variety  known  as  jewelers'  red  —  for  polishing  soft 
iron-carbon  alloys.  He  advises  that  the  commercial  preparation 
be  washed  before  use,  or,  still  better,  that  the  material  be  pre- 
pared by  the  user,  whereby  as  low  a  temperature  as  is  practicable 
should  be  maintained  in  firing  it.  He  obtained  especially  favor- 
able results  with  the  oxalate  red  (English  red  made  from  iron 
oxalate)  which  is  employed  in  mirror  factories.  If  aluminium 
oxide  is  used  in  polishing  (LeChatelier),  much  more  rapid  results 
are  obtained.  The  polishing  machine  used  by  Osmond  was  con- 
structed by  Fuess  of  Steiglitz,  near  Berlin.  A  piece  of  short 
fibered  cloth  is  stretched  upon  its  smoothly  machined  horizon- 
tal revolving  plate,  and  sprinkled  with  polishing  powder. 

Alloys  which  are  composed  of  costly  material  should  be  neither 
ground  nor  filed,  but  are  most  economically  shaped  by  sawing. 

§  2.   DEVELOPMENT  OP  STRUCTURE. 

If  the  separate  structure  elements  of  an  alloy  differ  in  color,  the 
structure  of  its  section  is  evident  at  a  glance.  A  good  example 
of  this  condition  is  to  be  found  in  the  gold-lead  series  investi- 
gated by  VoGEL.1 

In  case  the  different  structure  elements  vary  considerably  in 
hardness  or  elasticity,  it  is  possible  for  reliefs  to  appear  in  the 
finished  section,  owing  to  more  rapid  wearing  off  of  the  softer 
material  on  grinding  and  polishing.  In  general,  it  is  desirable  to 
avoid  this  effect,  since  the  difference  in  height  between  the  several 
structure  elements  after  the  sectior  is  prepared  may  be  great 
enough  to  prevent  sharp  focusing  under  the  microscope.  The 
method  of  grinding  and  polishing  outlined  above  is  capable  of 
1  VOGEL,  Z.  anorg.  Chem.,  45,  11  (1905). 


320  THE  ELEMENTS   OF   METALLOGRAPHY. 

producing  level  surfaces  if  carried  out  properly.  There  are, 
however,  methods  which  make  use  of  these  differences  between 
the  several  structure  elements  with  respect  to  mechanical  proper- 
ties, in  the  development  of  structure.  They  are,  namely,  "grind- 
ing in  relief,"1  and  "relief  polishing."2  The  latter  method  has 
proven  valuable  in  the  investigation  of  iron-carbon  alloys 
(compare  Table  6,  p.  237)  and  is  based  upon  the  use  of  an  elastic 
polishing  foundation,  e.g.,  of  parchment,  which  will  readily  adjust 
itself  to  the  resulting  irregularities  in  the  surface  of  the  section. 
In  polishing,  the  ordinary  polishing  materials  (such  as  jewelers' 
red)  are  used  with  water.  Relief  polishing  may  be  combined  with 
feeble  chemical  action  ("Etch-polishing").2  Quite  notably,  solu- 
tions may  be  used  in  this  connection  which  ordinarily  fail  to 
attack  iron,  for  example,  extract  of  licorice,  ammonia  water,  or, 
best  of  all,  a  2  per  cent  solution  of  ammonium  nitrate.  Etch- 
polishing  is  carried  out  in  the  same  manner  as  relief  polishing: 
one  of  these  solutions  replacing  water. 

In  the  main,  the  goal  is  most  quickly  reached  when  the  dif- 
fering chemical  properties  of  individual  structure  elements  are 
observed  in  the  development  of  structure.  Thus,  the  section  is 
"etched,"  i.e.,  it  is  treated  with  reagents  which  attack  the  differ- 
ent structure  elements  variously.  The  portions  which  are  most 
strongly  attacked  by  the  etching  agent  suffer  loss  of  their  property 
of  reflecting  light,  which  was  due  entirely  to  their  high  polish,  while 
the  more  or  less  unattacked  parts  retain  their  brilliancy.  In 
order  that  an  etching  agent  may  attack  the  material  uniformly,  it 
is  essential  that  the  latter  be  well  wet  by  the  liquid.  Therefore, 
the  section  must  first  be  freed  from  all  fatty  material.  This  con- 
dition is  secured  by  dipping  in  alcohol,  ether,  or  chloroform,  etc., 
after  which  a  clean  cloth  is  used  to  wipe  away  the  liquid.  Some 
consider  it  more  advisable  to  remove  grease  by  dry  rubbing  with 
Vienna  chalk  or  tin  ash,  which  material  may  be  applied  on  a  clean 
cloth  or  a  piece  of  fine  grained  wood. 

What  etching  agent  is  suitable  for  a  given  alloy  and  how  long  it 
should  be  allowed  to  act  are  matters  which  must  be  determined  by 
experiment.  For  this  purpose,  a  drop  of  the  liquid  to  be  tested 
is  placed  on  the  alloy  and  left  for  a  moment.  It  is  then  washed 

1  BEHRENS,  1.  c.,  p.  10. 

2  OSMOND,  Contribution  a  1'etude  des  alliages,  p.  280. 


INVESTIGATION   OF  STRUCTURES.  321 

off  and  the  section  examined  —  eventually  under  the  microscope. 
If  either  very  slight  action  or  none  at  all  is  observed,  etching  is 
allowed  to  continue  in  the  same  spot.  If  too  pronounced  etching 
is  noticed,  the  reagent  is  allowed  to  act  for  a  shorter  period  in 
another  spot,  or  it  is  further  diluted.  It  is  frequently  difficult  to 
find  a  proper  etching  agent.  Sometimes  the  structure  is  developed 
very  beautifully  by  over  etching  the  section  and  then  lightly 
repolishing  the  etched  spot. 

Etching  agents  which  are  commonly  used  are  the  ordinary  acids: 
nitric  acid,  sulphuric  acid  and  hydrochloric  acid,  in  concentrated 
form,  as  well  as  variously  diluted.  Solutions  of  the  acids  in  amyl 
alcohol  operate  very  slowly,  but  withal  very  evenly.  In  this  con- 
nection, 4  per  cent  solutions  of  nitric  acid  or  of  picric  acid  in  amyl 
alcohol  are  of  service  in  the  investigation  of  alloys  containing  iron. 
After  etching  with  picric  acid,  the  section  should  be  rinsed  with 
absolute  alcohol  and  wiped  with  a  soft  flannel  cloth.  Solutions 
of  the  various  acids  in  ethyl  alcohol  have  also  been  extensively 
used.  Etching  with  aqua  regia,  variously  diluted,  frequently 
yields  satisfactory  results  in  the  case  of  alloys  of  the  noble 
metals. 

Reference  has  already  been  made  to  the  use  of  tincture  of  iodine 
in  the  investigation  of  iron-carbon  alloys  (p.  237).  According  to 
Osmond,  this  mixture  should  not  be  prepared  with  absolute  alco- 
hol. The  tincture  ordinarily  used  in  medicine  is  of  the  proper  con- 
centration. He  applies  it  gradually  with  the  finger  until  about  a 
drop  per  square  centimeter  has  been  added.  Etching  proceeds 
until  the  color  of  the  tincture  disappears.  If  necessary,  the  process 
is  repeated.  When  etched  sufficiently,  the  section  is  rinsed  with 
alcohol  and  dried  with  a  fine  dry  linen  cloth.  A  blast  of  air  is 
even  better  for  drying. 

An  aqueous  solution  of  copper-ammonium  chloride  has  also  been 
used  largely  for  etching  — e.g.,  in  the  investigation  of  antimony- 
bismuth  alloys  by  Hiittner  and  Tammann.  They  were  able  in 
this  way  to  distinguish  the  antimony  rich  crystals  (only  slightly 
attacked  in  the  cold  by  a  dilute  solution  as  above)  from  the  bis- 
muth rich  crystals  (much  more  strongly  attacked  by  this  etching 
agent). 

In  other  cases,  etching  by  means  of  alkaline  solutions  brings 
about  the  desired  end.  Thus,  Vogel  obtained  good  contrasts  in  the 


322  THE   ELEMENTS   OF   METALLOGRAPHY. 

case  of  gold-antimony  alloys  of  high  gold  concentration  by  long 
continued  action  of  sodium  hydroxide  solutions.  Again,  in  the 
cases  of  zinc  alloys,  aluminium  alloys  and  silicium  alloys,  this 
etching  agent  has  been  used  to  good  effect. 

Ammonia  should  be  tried  on  copper  alloys.  Addition  of  hydro- 
gen peroxide  hastens  its  action  as  a  rule. 

LECHATELiER1  uses  the  electric  current  for  etching,  in  that  the 
alloy  under  investigation  is  made  the  anode  in  a  circuit.  Oper- 
ating under  a  current  density  of  1/1000  to  I/ 100  amperes  per  square 
centimeter,  only  the  least  resistant  structure  elements  are  etched 
in  from  1  to  10  minutes.  A  lesser  current  density  is  to  be  chosen  in 
proportion  as  the  different  structure  elements  approach  one  another 
in  their  tendency  to  become  etched.  It  is  not  advisable,  however, 
to  use  a  current  density  of  less  than  1/1000  amperes  per  square 
centimeter,  since,  otherwise,  non-uniform  distribution  of  the 
current  over  the  surface  of  the  section  is  likely  to  result.  An 
aqueous  salt  solution  which  does  not  attack  the  alloy  when  no 
current  is  passing  is  used  as  electrolyte.  In  most  cases  ammonium 
nitrate  was  chosen  by  LeChatelier.  Now  and  then,  etching 
appeared  very  plainly  when  a  salt  giving  a  precipitate  with  the 
metal  in  question  was  added  to  the  electrolyte  —  for  example, 
in  the  case  of  copper,  potassium  ferrocyanide  or  potassium  thio- 
cyanate. 

In  many  cases  a  section  becomes  etched  simply  on  standing  in 
the  air,  i.e.,  it  "  tarnishes. "  Obviously,  such  ready  oxidation 
of  an  alloy  considerably  hinders  investigation  of  its  structure. 
Sometimes  it  is  impossible  to  polish  the  section.  Oxidation  of  a 
single  constituent  of  the  alloy  may  occur,  and  even  that  may 
require  moisture.  Such  sections  are  preserved,  after  being  etched 
sufficiently  on  exposure  to  the  air  (which  always  contains  water 
vapor),  by  enclosing  them  in  a  desiccator. 

If  oxidation  does  not  proceed  with  sufficient  rapidity  at  ordinary 
temperature,  it  may  be  hastened  by  heating.  The  section,  dry 
and  free  from  grease,  is  heated  upon  an  iron  plate  or  sand  bath 
until  the  desired  surface  colors  (interference  colors  caused  by  thin 
layers  of  oxide)  appear.  It  is  then  cooled  off  with  all  possible 
rapidity.  Some  practice  is  necessary  in  order  to  properly  carry 
out  this  process. 

1  LECHATELIER,  Contribution  a  l'6tude  des  alliages,  p.  67. 


INVESTIGATION  OF  STRUCTURES. 


323 


§  3.   MICROSCOPICAL  INVESTIGATION. 

Metallic  sections  are  capable  of  investigation  in  reflected  light 
alone,  owing  to  their  opacity.  If  light  is  allowed  to  fall  in  an 
oblique  direction  upon  a  perfectly  mirrored  surface,  no  rays  will 
enter  a  microscope,  the  optical  axis  of  which  is  perpendicular  to 
the  reflecting  surface  (Fig.  117,  a),  i.e.,  the  latter  will  appear  dark. 
In  order  that  the  reflecting  surface  may  appear  bright,  it  is 
necessary  to  adjust  the  optical  axis  of  the  microscope  obliquely 


to  it  in  the  direction  of  the  reflected  rays  (Fig.  117,  6).  On  the 
other  hand,  if  the  rays  of  light  fall  perpendicularly  upon  the 
reflecting  surface,  the  latter  will  appear  light  through  a  micro- 
scope, the  optical  axis  of  which  is  perpendicular  to  the  surface 
(Fig.  117,  c).  On  directing  light  upon  a  diffusely  reflecting  surface, 
a  rather  unchangeable  fraction  enters  the  microscope,  however 
the  latter  may  be  arranged  with  respect  to  the  direction  of  the 
original  beam.  Relative  to  the  appearance  of  a  section  which, 
although  originally  polished  to  a  mirror-like  surface,  has  lost  its 
luster  in  certain  places  through  etching,  the  following  may  be 
said:  Under  the  arrangement  given  in  Fig.  117,  a,  no  light  enters 
the  microscope  from  the  " mirrored"  portions,  but  the  " non- 
mirrored"  portions  send  diffuse  light  into  the  microscope.  The 
portions  which  have  not  been  etched  appear  dark,  and  those  which 
have  been  etched  appear  light.  Under  the  arrangements  shown  in 
Fig.  117,  6  and  c,  all  of  the  light  which  falls  upon  the  unetched 
(completely  reflecting)  portions  enters  the  microscope,  and  these 
portions  consequently  appear  lighter  than  the  diffusely  reflecting 


324 


THE  ELEMENTS   OF   METALLOGRAPHY. 


portions,  although  the  sum  total  of  light  which  enters  the  micro- 
scope from  the  latter  source  is  about  the  same  as  under  the  arrange- 
ment given  in  Fig.  117,  a. 

An  arrangement  such  as  that  indicated  in  Fig.  117,  a,  is  readily 
attained  with  ordinary  appliances.  A  common  microscope  with 
a  rigid  stand  may  be  used  in  making  observations.  The  oblique 
bundle  of  light  rays  may  be  obtained  by  means  of  a  simple  or 
compound  lense  properly  set  up.  Since  very  little  light,  namely, 
only  that  which  comes  from  the  diffusely  reflecting  portions  of  the 
section,  enters  the  microscope,  low  magnifications  must  be  used. 
The  arrangement  indicated  in  Fig.  117,  6,  requires  a  microscope 
stand  by  means  of  which  the  instrument  may  be  placed  in  any 
inclined  position.  The  Martens  ball  microscope  stand,  so  called 
owing  to  the  use  of  ball  joints  in  securing  the  requisite  flexibility, 
is  of  this  description.  This  arrangement  is  also  unsuited  to  high 
powers  of  magnification,  notwithstanding  the  large  amount  of 
light  which  enters  the  microscope,  since  the  varying  distance  of 
different  parts  of  the  illuminated  surface 
from  the  objective  (on-  account  of  its  in- 
clination to  the  axis*  of  the  instrument) 
precludes  all  possibility  of  a  sharp  focus 
with  objectives  of  short  focal  distance. 
Obviously,  the  arrangement  indicated  in 
Fig.  117,  c,  may  be  realized  with  the  Martens 
stand. 

It  is  thus  evident  that  for  higher  mag- 
nifications the  arrangement  shown  in  Fig. 
117,  c,  which  assigns  a  vertical  position  to 
the  microscope  and  perpendicular  incidence 
to  the  light  rays,  is  alone  open  to  con- 
sideration. The  latter  is  effected  by  means 
of  a  vertical  illuminator.  This  consists 
essentially  of  a  glass  prism  A  (see  Fig. 
118)  placed  between  objective  and  ocular  in  such  a  way  that 
its  extreme  (inside)  edge  reaches  only  to  the  optical  axis  of  the 
microscope.  A  given  ray  from  a  beam  of  light  which  enters  on 
the  side  at  B  and  is  cut  down  to  the  requisite  size  at  this  point 
by  an  iris  diaphragm  is  totally  reflected  downwards  through  the 
prism,  deflected  by  the  objective  C  so  that  it  falls  upon  the  object 


FIG.  118.    Vertical 
Illuminator. 


INVESTIGATION  OF  STRUCTURES. 


325 


D  under  investigation,  reflected  from  the  surface  of  the  object, 
and  deflected  again  by  the  objective,  whence  it  proceeds  to  the 
ocular  in  a  direction  parallel  to  the  optical  axis. 

The  construction  of  a  microscope  for  this  purpose  calls  for 
nothing  unusual  and  is  governed  by  the  desired  magnification  and 
sharpness  of  image.  The  microscope  used  at  the  Goettingen 
Institute  was  constructed  at  the  optical  works  of  R.  Winkel  at 
Goettingen  for  magnifications  of  18,  60,  140,  310  and  640  times. 

§  4.     PHOTOGRAPHY. 

Metallic  sections  may  be  photographed  by  removing  the  ocular 
from  the  microscope  and  substituting  a  suitable  photographic 
camera.  Naturally,  the  section  is  first  placed  to  advantage,  as 
regards  the  portion  of  the  surface  to  be  photographed,  by  direct 
test  observations  under  the  ocular.  The  frequent  exchange  of 
ocular  and  camera  which  is  necessary  under  these  conditions, 
becomes  a  burden  and  is  dispensed  with  in  the  arrangement  given 
by  LfiCn ATELIER.1  This  arrangement  consists  in  a  combination 
of  ocular  A  and  camera  B  (Fig.  119,  a),  the  optical  axes  of  which 


H 


FIG.  119.     Microscope  according  to  LeChatelier. 

are  both  horizontal  and  stand  at  right  angles  to  each  other,  with 
a  single  objective  C,  the  optical  axis  of  which  is  vertical.  The 
latter  axis  is  therefore  at  right  angles  to  the  first  two  axes,  and 
the  three  optical  axes  are  disposed  in  such  a  way  as  to  constitute 
a  right  angled  coordinate  system.  The  necessary  deflection  of 

1  LECHATELIER,  contribution  £  l'£tude  des  alliages,  p.  431. 


326  THE   ELEMENTS   OF   METALLOGRAPHY. 

the  light  rays  is  effected  by  two  total  reflecting  prisms  D  and  E, 
which  are  so  placed  in  Fig.  119,  b,  that  light  would  enter  the  camera 
B.  A  ray  of  light  which  is  passed  through  the  illumination  tube 
F  in  a  direction  parallel  to  its  axis  falls  upon  the  prism  E,  in  which 
it  is  totally  reflected  upwards.  In  this  manner,  it  reaches  the 
objective  C,  where  it  is  deflected  to  fall  upon  the  lower  side  of  the 
object  B.  At  this  point,  it  is  reflected  and  again  deflected  on 
repassing  C.  The  ray  is  now  directed  at  right  angles  towards 
the  prism  D  (below),  where  it  is  totally  reflected  in  the  direction 
of  the  camera  B.  If  the  prism  D  is  now  turned  90  degrees  around 
the  vertical  axis  J,  it  directs  the  light  ray  toward  the  ocular 
A,  which  is  situated  at  right  angles  to  B.  The  latter  course  can- 
not be  followed  on  the  diagram  since  it  is  at  right  angles  to  the 
plane  of  the  paper  (A  is  not  shown  in  Fig.  119,  6).  The  perforated 
object  table  G  is  adjustable.  For  photographing,  a  section  is 
placed  on  the  object  table  with  its  prepared  surface  downwards. 
The  prism  D  is  turned  so  that  light  enters  the  ocular,  and  a 
suitable  part  of  the  surface  of  the  section  is  sought  out.  Then 
the  light  rays  are  directed  into  the  camera  by  turning  the 
prism. 

The  ordinary  methods  of  photography  are  carried  out  in  the 
present  connection.  Obviously,  the  time  of  exposure  depends 
upon  the  strength  of  light  from  the  source  of  illumination.  At  the 
Goettingen  Institute,  a  Nernst  lamp  (large  model)  L  is  preferably 
used  for  this  purpose.  In  order  to  obviate  the  disturbing  action 
of  side  lights,  a  perforated  plate  K  is  placed  between  the  illumi- 
nating source  and  the  tube  F.  The  time  of  exposure  approxi- 
mates 10  minutes  under  these  conditions.  If  an  arc  lamp  is  used, 
only  a  few  seconds  exposure  are  required.  The  latter  is  not  to  be 
recommended  since,  on  account  of  the  irregular  action  of  such  a 
lamp,  the  intensity  of  its  light  varies  considerably. 

After  exposure,  the  plate  is  developed  in  the  usual  manner, 
fixed  in  an  acid  fixing  bath,  thoroughly  washed,  and  then  used 
for  preparation  of  a  positive.  In  case  the  contrasts  in  the  object 
to  be  photographed  are  very  delicate,  Vogel-Obernetter's  eosine 
plates  (prepared  by  Otto  Perutz,  Muenchen),  which  are  very  sen- 
sitive to  colors,  will  be  found  very  serviceable.  Contrasts  appear 
best  on  short  exposure.  Glossy  paper  is  most  satisfactory  in 
printing  from  the  negative.  If  contrasts  are  not  well  marked  in 


INVESTIGATION   OF  STRUCTURES.  327 

the  negative,  good  prints  may  be  made  on  " Rembrandt"  paper, 
which  should  be  printed  to  a  dark  bronze  color.  Directions  for 
drying  and  fixing  accompany  the  different  brands  of  printing 
paper. 

CONCLUSION. 

In  conclusion,  we  will  introduce  a  few  remarks  relative  to  the 
practical  significance  of  the  methods  described  in  this  book,  and 
the  results  obtained  by  their  use.  In  estimating  the  service  which 
METALLOGRAPHY  has  rendered  in  the  realm  of  its  application,  we 
must  not  fail  to  recognize  that  the  time  during  which  metallic 
alloys  have  been  used  without  any  particular  need  of  inquiring 
into  their  constitution  has  been  incomparably  long  as  opposed  to 
the  few  years  during  which  successful  scientific  revision  of  this 
field  has  taken  place.  If,  therefore,  we  are  unable  to  report,  at 
this  juncture,  any  revolutionary  innovation  in  the  metal  industry 
field  due  to  metallographical  investigation,  yet  the  advancement 
along  technical  lines  which  has  already  been  brought  about  by 
this  infant  branch  of  science  seems  worthy  of  consideration  in  the 
highest  degree.  METALLOGRAPHY  first  of  all  furnishes  us  with  a 
means  for  judging  a  product  in  cases  where  chemical  analysis  fails 
of  application,  and  is,  in  consequence,  a  valuable  agent  in  the  test- 
ing of  materials  and  in  the  regulation  of  factory  products.  We 
have  seen,  in  discussing  the  iron-carbon  diagram,  how  much  the 
properties  of  two  alloys  of  the  same  chemical  composition  may 
differ  from  one  another.  To  one  acquainted  with  the  structure 
of  iron-carbon  alloys,  microscopical  investigation  of  a  section  is 
capable  of  showing  at  once  whether  the  material  in  hand  possesses 
the  desired  properties  or  not. 

If  the  properties  of  the  various  structure  elements  composing  a 
system  are  known,  a  glance  at  the  perfected  diagram  serves  to 
indicate  how  one  should  proceed  to  vary  the  properties  of  an  alloy 
of  given  composition  within  possible  limits  — r  also  shown  by  the 
diagram.  We  are  already  close  upon  this  goal  in  the  especial  case 
of  iron-carbon  alloys.  The  temperature  to  which  a  variety  of 
iron  of  definite  carbon  content  should  be  heated,  the  temperature 
range  within  which  it  should  be  held  for  a  time  on  cooling,  and 
that  through  which  it  should  be  conducted  with  all  possible  rapid- 
ity in  order  to  obtain  this  or  that  variety  of  steel  —  all  this  infor- 


328  THE  ELEMENTS   OF   METALLOGRAPHY. 

mation  may  be  taken  directly  from  the  diagram,  which  embraces 
the  results  of  our  experience  in  these  matters  in  the  most  concise 
and  clear  manner.  The  enhanced  trustworthiness  of  manu- 
facture when  managed  on  such  a  basis  will  not  be  held  cheaply 
by  any  technical  worker. 

Again  the  rationally  progressive  investigator  in  this  field  will 
scarcely  be  able  to  do  without  a  knowledge  of  the  constitution  of 
metallic  alloys,  whether  he  has  the  intention  of  realizing  processes 
which  are  already  current  with  cheaper  materials  or  by  cheaper 
methods,  or  is  aiming  to  adjust  new  demands  to  a  certain  kind  of 
material.  The  melting-point  diagram  shows  him  the  predominant 
concentrations,  such  as  limits  of  miscibility,  eutectica,  etc.,  whence 
it  is  merely  necessary  for  him  to  investigate  the  properties  of  alloys 
corresponding  to  these  and  to  several  intermediate  concentrations 
in  order  to  learn  whether  a  certain  course  entered  upon  may  be 
expected  to  realize  the  end  in  view  or  not.  Thus,  well  directed 
experimental  effort  is  substituted  for  aimless  probing  and  testing. 
Charpy's  investigation  of  bearing  metals,  which  was  mentioned 
on  page  275,  furnishes  a  standard  illustration  of  this. 

The  metallic  alloys  of  greatest  technical  importance  are  radi- 
cally those,  the  components  of  which  are  appreciably  miscible  in 
the  crystalline  condition.  Experience  teaches  us  that  a  metal 
which  in  the  crystalline  condition  contains  a  dissolved  amount  — 
even  though  small  —  of  another  substance,  frequently  exhibits 
properties  —  hardness,  tensile  strength,  conductivity,  etc.,  which 
are  quite  widely  at  variance  with  those  of  the  pure  metal.  Experi- 
ments dealing  with  the  quantitative  aspect  of  these  effects  are 
already  on  record.  C.  BENEDICKS*  arrives  at  the  conclusion  that 
different  elements  when  dissolved  in  equivalent  quantities  in  iron 
raise  its  specific  conductivity  to  the  same  extent.  Concerning 
the  influence  of  dissolved  material  on  the  hardness  of  iron,  some- 
what similar,  although  less  simple,  relations  were  found. 

Although  we  stand  at  the  present  time  on  the  threshold  of  a 
process  of  development,  it  may,  nevertheless,  be  held  most  prob- 
able that  technical  progress  in  the  metallic  alloy  field  will  proceed 
henceforth  lesser  in  an  empirical  manner  than  on  the  basis  of  exact 
knowledge  of  their  constitution. 

1  BENEDICKS,  Recherches  physiques  et  physicochimiques  sur  Tacier  au 
carbone.  Upsala,  1904. 


INVESTIGATION  OF  STRUCTURES.  329 

Collection  of  references  to  Binary  Fusion  Diagrams  of  the  Metallic 
Elements,  covering  such  elements  as  have  received  more  or  less 
extended  attention  in  this  respect  (all  of  the  common  metals  and 
many  which,  although  not  rare,  are  commercially  unimportant). 

1.   SODIUM. 

1.  Na-K.     Kurnakow  and  Puschin Z.  anorg.  Chem.,  30,  109,  (1902). 

2.  (Na-Cu). 

3.  (Na-Ag). 

4.  (Na-Au). 

5.  Na-Mg.     Mathewson Z.  anorg.  Chem.,  48,  191,  (1906). 

6.  Na-Zn.     Mathewson Z.  anorg.  Chem.,  48,  101,  (1906). 

7.  Na-Cd.     Mathewson Z.  anorg.  Chem.,  50,  171,  (1906). 

8.  Na-Hg.    Schiillar Z.  anorg.  Chem.,  40,  3,  (1904). 

9.  Na-Al.     Mathewson Z.  anorg.  Chem.,  48,  191,  (1906). 

10.  Na-Tl.      Kurnakow  and  Puschin. .  .  .Z.  anorg.  Chem.,  30,  86,  (1902). 

11.  (Na-Si). 

12.  Na-Sn.     Mathewson Z.  anorg.  Chem.,  46,  94,  (1905). 

13.  Na-Pb.    Mathewson Z.  anorg.  Chem.,  50,  171,  (1906). 

14.  Na-Sb.     Mathewson Z.  anorg.  Chem.,  50,  171,  (1906). 

15.  Na-Bi.     Mathewson Z.  anorg.  Chem.,  50,  171,  (1906). 

16.  (Na-Cr). 

17.  (Na-Te). 

18.  (Na-Mn). 

19.  (Na-Fe). 

20.  (Na-Co). 

21.  (Na-Ni). 

22.  (Na-Pd). 

23.  (Na-Pt). 

2.  POTASSIUM. 

24.  (K-Cu). 

25.  (K-Ag). 

26.  (K-Au). 

27.  K-Mg.    Smith Z.  anorg.  Chem.,  56,  109,  (1907). 

28.  K-Zn.     Smith Z.  anorg.  Chem.,  56,  109,  (1907). 

29.  K-Cd.    Smith Z.  anorg.  Chem.,  56,  109,  (1907). 

30.  K-Hg.    Janecke Z.  phys.  Chem.,  58,  245,  (1907). 

31.  K-A1.     Smith Z.  anorg.  Chem.,  56,  109,  (1907). 

32.  K-T1.     Kurnakow  and  Puschin Z.  anorg.  Chem.,  30,  86,  (1902). 

33.  (K-Si). 

34.  K-Sn.     Smith Z.  anorg.  Chem.,  56,  109,  (1907). 

35.  K-Pb.     Smith Z.  anorg.  Chem.,  56,  109,  (1907). 

36.  (K-Sb). 


330 


THE   ELEMENTS   OF   METALLOGRAPHY. 


37. 

38. 
39. 
40. 
41. 
42. 
43. 
44. 
45. 


K-Bi.     Smith.  . 

(K-Cr). 

(K-Te). 

(K-Mn). 

(K-Fe). 

(K-Co). 

(K-Ni). 

(K-Pd). 

(K-Pt). 


,Z.  anorg.  Chem.,  56,  109,  (1907). 


3.   COPPER. 


46.  Cu-Ag.     Heycock  and  Neville Trans.  Royal  Soc.,  189,  25,  (1897). 

Friedrich  and  Leroux Metallurgie,  4,  293,  (1907). 

47.  Cu-Au.     KurnakowandZemczuznyj.Z.  anorg.  Chem.,  54,  149,  (1907). 

48.  Cu-Mg.     Sahmen Z.  anorg  Chem.,  57,  1,  (1908). 

49.  Cu-Zn.     Shepherd J.  Phya.  Chem.,  8,  421,  (1904). 

Tafel. Metallurgie,  5,  343,  (1908),  et  seq. 

50.  Cu-Cd.      Sahmen Z.  anorg.  Chem.,  49,  301,  (1906). 

51.  (Cu-Hg). 

52.  Cu-Al.      Gwyer Z.  anorg.  Chem.,  57,  113,  (1908). 

53.  Cu-Tl.     Doerinckel Z.  anorg.  Chem.,  48,  185,  (1906). 

54.  Cu-Si.      Rudolf i Z.  anorg.  Chem.,  53,  216,  (1907). 

55.  Cu-Sn.     Shepherd  and  Blough J.  Phys.  Chem.,  10,  630,  (1906). 

56.  Cu-Pb.     Hiorns J.  Soc.  Chem.  Ind.,  25,  616,  (1906). 

Friedrich  and  Leroux Metallurgie,  4,  293,  (1907). 

57.  Cu-Sb.     Baikow J.  Russ.  Phys.  Chem.  Soc.,  36,  111 

(1905).     Bull.  soc.  encouragement, 
200,  (1903);  C.  B.,  1905  (1),  665. 

58.  Cu-Bi.      Jeriomin. . Z.  anorg.  Chem.,  55,  412,  (1907). 

59.  Cu-Cr.      Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 

60.  Cu-Te.      Chikashige Z.  anorg.  Chem.,  54,  50,  (1907). 

61.  Cu-Mn.     Wologdine Revue  de  Met.,  4,  27,  (1907). 

Sahmen Z.  anorg.  Chem.,  57,  1,  (1908). 

Zemczuznyj,    Urasow    and 

Rykowskow Z.  anorg.  Chem.,  57,  253,  (1908). 

62.  Cu-Fe.      Sahmen Z.  anorg.  Chem.,  57,  1,  (1908). 

63.  Cu-Co.      Sahmen Z.  anorg.  Chem.,  57,  1,  (1908). 

64.  Cu-Ni.      Guertler  and  Tammann..  .  .Z.  anorg.  Chem.,  52,  25,  (1907). 

Kurnakow and  Zemczuznyj  Z.  anorg.  Chem.,  54,  149,  (1907). 

65.  Cu-Pd.     Ruer Z.  anorg.  Chem.,  51,  223,  (1906). 

66.  Cu-Pt.      Doerinckel Z.  anorg.  Chem.,  54,  333,  (1907). 

4.   SILVER. 

67.  Ag-Au.     Roberts- Austin  and  Kirke 

Rose Chem.  News,  87,  2,  (1903). 

68.  Ag-Mg.     Zemczuznyj Z.  anorg.  Chem.,  49,  400,  (1906). 

69.  Ag-Zn.      Petrenko Z.  anorg.  Chem.,  48,  347,  (1906). 


INVESTIGATION  OF  STRUCTURES.  331 

70.  Ag-Cd.  Rose Proc.  Royal  Soc.,  74,  218. 

71.  (Ag-Hg). 

72.  Ag-Al.  Petrenko Z.  anorg.  Chem.,  46,  49,  (1905). 

73.  Ag-Tl.  Petrenko Z.  anorg.  Chem.,  50,  133,  (1906). 

74.  Ag-Si.  Arrivant Z.  anorg.  Chem.,  60,  436,  (1908). 

75.  Ag-Sn.  Petrenko Z.  anorg.  Chem.,  53,  200,  (1907). 

76.  Ag-Pb.  Petrenko Z.  anorg.  Chem.,  53,  200,  (1907). 

Friedrich  and  Leroux Metallurgie,  4,  293,  (1907). 

77.  Ag-Sb.     Petrenko Z.  anorg.  Chem.,  50,  133,  (1906). 

78.  Ag-Bi.      Petrenko Z.  anorg.  Chem.,  50,  133,  (1906). 

79.  Ag-Cr.      Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 

80.  (Ag-Te). 

81.  Ag-Mn.      Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 

82.  Ag-Fe.       Petrenko Z.  anorg.  Chem.,  53,  212,  (1907). 

83.  Ag-Co.       Petrenko Z.  anorg.  Chem.,  53,  212,  (1907). 

84.  Ag-Ni.       Petrenko Z.  anorg.  Chem.,  53,  212,  (1907). 

85.  Ag-Pd.      Ruer Z.  anorg.  Chem.,  51,  315,  (1906). 

86.  Ag-Pt.      Doerinckel Z.  anorg.  Chem.,  54,  333,  (1907). 

5.    GOLD. 

87.  (Au-Mg). 

88.  Au-Zn.     Vogel Z.  anorg.  Chem.,  48,  319,  (1906). 

89.  Au-Cd.     Vogel Z.  anorg.  Chem.,  48,  333,  (1906). 

90.  (Au-Hg). 

91.  Au-Al.     Heycock  and  Neville Trans.    Royal    Soc.,    194    (A),    201, 

(1900). 

92.  Au-Tl.      Levin Z.  anorg.  Chem.,  45,  31,  (1905). 

93.  (Au-Si). 

94.  Au-Sn.     Vogel Z.  anorg.  Chem.,  46,  60,  (1905). 

95.  Au-Pb.     Vogel Z.  anorg.  Chem.,  45,  11,  (1905). 

96.  Au-Sb.     Vogel Z.  anorg.  Chem.,  50,  145,  (1906). 

97.  Au-Bi.     Vogel Z.  anorg.  Chem.,  50,  145,  (1906). 

98.  (Au-Cr). 

99.  (Au-Te). 

100.  (Au-Mn). 

101.  Au-Fe.     Isaac  and  Tammann Z.  anorg.  Chem.,  53,  281,  (1907). 

102.  (Au-Co). 

103.  Au-Ni.     Levin Z.  anorg.  Chem.,  45,  238,  (1905). 

104.  Au-Pd.    Ruer Z.  anorg.  Chem.,  51,  391,  (1906). 

105.  Au-Pt.     Doerinckel Z.  anorg.  Chem.,  54,  333,  (1907). 

6.   MAGNESIUM. 

106.  Mg-Zn.     Grube Z.  anorg.  Chem.,  49,  72,  (1906). 

107.  Mg-Cd.     Grube Z.  anorg.  Chem.,  49,  72,  (1906). 

108.  (Mg-Hg). 

109.  Mg-Al.      Grube Z.  anorg.  Chem.,  45,  225,  (1905). 


332 


THE  ELEMENTS   OF   METALLOGRAPHY. 


110.  Mg-Tl.      Grube Z.  anorg.  Chem.,  46,  76,  (1905). 

111.  Mg-Si.      Vogel Z.  anorg.  Chem.,  61,  46,  (1909). 

112.  Mg-Sn.     Grube Z.  anorg.  Chem.,  46,  76,  (1905). 

113.  Mg-Pb.     Grube Z.  anorg.  Chem.,  44,  117,  (1905). 

114.  Mg-Sb.     Grube Z.  anorg.  Chem.,  49,  72,  (1906). 

115.  Mg-Bi.      Grube Z.  anorg.  Chem.,  49,  72,  (1906). 

116.  (Mg-Cr). 

117.  (Mg-Te). 

118.  (Mg-Mn). 

119.  (Mg-Fe). 

120.  (Mg-Co). 

121.  (Mg-Ni).     Voss Z.  anorg.  Chem.,  57,  34,  (1908). 

122.  (Mg-Pd). 

123.  (Mg-Pt). 

7.  ZINC. 

124.  Zn-Cd.  Hindrichs Z.  anorg.  Chem.,  55,  415,  (1907). 

125.  Zn-Hg.  Puschin Z.  anorg.  Chem.,  36,  201,  (1903). 

126.  Zn-Al.  Shepherd J.  Phys.  Chem.,  9,  504,  (1905). 

127.  Zn-Tl.  Vegesack Z.  anorg.  Chem.,  52,  30,  (1907). 

128.  (Zn-Si). 

129.  Zn-Sn.  Heycock  and  Neville J.  Chem.  Soc.,  383,  (1897). 

130.  Zn-Pb.  Spring  and  Romanoff  .  .  .Z.  anorg.  Chem.,  13,  29,  (1897). 

Heycock  and  Neville  .  .  .  .J.  Chem.  Soc.,  71,  383,  (1897). 

131.  Zn-Sb.       Monckemeyer Z.  anorg.  Chem.,  43,  182,  (1905). 

Zemczuznyj Z.  anorg.  Chem.,  49,  384,  (1906). 

132.  Zn-Bi.        Spring  and  Romanoff  .  .  .Z.  anorg.  Chem.,  13,  29,  (1897). 

Heycock  and  Neville  .  . .  .  J.  Chem.  Soc.,  71,  383,  (1897). 

133.  Zn-Cr.       Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 

134.  (Zn-Te). 

135.  (Zn-Mn). 

136.  Zn-Fe.      Vegesack Z.  anorg.  Chem.,  52,  30,  (1907). 

137.  Zn-Co.       Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

138.  Zn-Ni.       Tafel Metallurgie,  4,   781,    (1907)    and   5, 

343,  (1908)  et  seq. 
Voss Z.  anorg.  Chem.,  57,  34,  (1908). 

139.  (Zn-Pd). 

140.  (Zn-Pt). 

8.  CADMIUM. 

141.  Cd-Hg.     Bijl Z.  Phys.  Chem.,  41,  641,  (1902). 

Janecke Z.  Phys.  Chem.,  50,  399,  (1907). 

142.  Cd-Al.      Gwyer Z.  anorg.  Chem.,  57,  113,  (1908). 

143.  Cd-Tl.      Kurnakow  and  Puschin  .  .Z.  anorg.  Chem.,  30,  86,  (1902). 

144.  (Cd-Si). 

145.  Cd-Sn.     Stoffel Z.  anorg.  Chem.,  53,  137,  (1907). 


INVESTIGATION   OF  STRUCTURES. 


333 


146.  Cd-Pb. 

147.  Cd-Sb. 

148.  Cd-Bi. 


149. 
150. 
151. 
152. 
153. 
154. 
155. 
156. 


Cd-Cr. 

(Cd-Te). 

(Cd-Mn) 

Cd-Fe. 

Cd-Co. 

Cd-Ni. 

(Cd-Pd). 

(Cd-Pt). 


Stoffel Z.  anorg.  Chem.,  53,  152,  (1907). 

Janecite Z.  Phys.  Chem.,  50,  399,  (1907). 

Treitschke Z.  anorg.  Chem.,  50,  217,  (1906). 

Kurnakow  and  Konstanti- 

now Z.  anorg.  Chem.,  58,  1,  (1908). 

Stoffel Z.  anorg.  Chem.,  53,  137,  (1907). 

Portevin Revue  Met.,  4,  389,  (1907). 

Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 


Isaac  and  Tammann  .  .  .  .Z.  anorg.  Chem.,  55,  58,  (1907). 

Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

Voss Z.  anorg.  Chem.,  57,  34,  (1908). 


157. 
158. 


Hg-Al. 
Hg-Tl. 

159.  (Hg-Si). 

160.  Hg-Sn. 

161.  Hg-Pb. 


9.    MERCURY. 


Kurnakow  and  Puschin. .  .Z.  anorg.  Chem.,  30,  86,  (1902). 


Van  Heteren Z.  anorg.  Chem.,  42,  129,  (1904). 

Fay  and  North Am.  Chem.  J.,  25,  230,  (1901). 

Puschin Z.  anorg.  Chem.,  36,  209,(1903). 

Janecke Z.  Phys.  Chem.,  50,  399,  (1907). 

162.  (Hg-Sb). 

163.  Hg-Bi.     Puschin Z.  anorg.  Chem.,  36,  201,  (1903). 

164.  (Hg-Cr). 

165.  (Hg-Tc). 

166.  (Hg-Mn). 

167.  (Hg-Fe). 

168.  (Hg-Co). 

169.  (Hg-Ni). 

170.  (Hg-Pd). 

171.  (Hg-Pt). 


10.   ALUMINIUM. 

172.  A1-T1.     Doerinckel Z.  anorg.  Chem.,  48,  185,  (1906). 

173.  Al-Si.      Fraenkel Z.  anorg.  Chem.,  58,  154,  (1908). 

174.  Al-Sn.     Gwyer Z.  anorg.  Chem.,  49,  311,  (1906). 

175.  Al-Pb.     Gwyer Z.  anorg.  Chem.,  57,  113,  (1908). 

176.  Al-Sb.      Tammann Z.  anorg.  Chem.,  48,  53,  (1905). 

177.  Al-Bi.      Gwyer Z.  anorg.  Chem.,  49,  311,  (1906). 

178.  Al-Cr.      Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 

179.  (Al-Te). 

180.  Al-Mn.     Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 


334 


THE  ELEMENTS   OF  METALLOGRAPHY. 


181.  Al-Fe.      Carpenter  and  Edwards  .  .Engineering,  83,  253,  (1907). 

Gwyer Z.  anorg.  Chem.,  57,  113,  (1908). 

Curry Metallurgie,  5,  540,  (1908),  detailed 

abstract  with  fusion  diagram. 

182.  Al-Co.       Gwyer Z.  anorg.  Chem.,  57,  113,  (1908). 

183.  Al-Ni.       Gwyer Z.  anorg.  Chem.,  57,  113,  (1908). 

184.  (Al-Pd). 

185.  (Al-Pt). 

11.  THALLIUM. 

186.  Tl-Si.      Tamaru Z.  anorg.  Chem.,  61,  40,  (1909). 

187.  Tl-Sn.     Kurnakow  and  Puschin. .  .Z.  anorg.  Chem.,  30,  86,  (1902). 

188.  Tl-Pb.     Kurnakow  and  Puschin. .  .Z.  anorg.  Chem.,  52,  430,  (1907). 

Lewkonja Z.  anorg.  Chem.,  52,  452,  (1907). 

189.  Tl-Sb.     Williams Z.  anorg.  Chem.,  50,  127,  (1906). 

190.  Tl-Bi.      Chikashige Z.  anorg.  Chem.,  51,  328,  (1906). 

191.  (Tl-Cr). 

192.  Tl-Te.     Pelabon Cr.,  145,  118,  (1907). 

193.  (Tl-Mn). 

194.  Tl-Fe.     Isaac  and  Tammann Z.  anorg.  Chem.,  55,  58,  (1907). 

195.  Tl-Co.    Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

196.  Tl-Ni.    Voss Z.  anorg.  Chem.,  57,  34,  (1908). 

197.  (Tl-Pd). 

198.  (Tl-Pt). 

12.  SILICON. 

199.  Si-Sn.     Tamaru Z.  anorg.  Chem.,  61,  40,  (1909). 

200.  Si-Pb.     Tamaru Z.  anorg.  Chem.,  61,  40,  (1909). 

201.  Si-Sb.     Williams Z.  anorg.  Chem.,  55,  1,  (1907). 

202.  Si-Bi.      Williams Z.  anorg.  Chem.,  55,  1,  (1907). 

203.  (Si-Cr). 

204.  (Si-Te). 

205.  Si-Mn.     Doerinckel Z.  anorg.  Chem.,  50,  117,  (1906). 

206.  Si-Fe.      Guertler  and  Tammann .  .  .Z.  anorg.  Chem.,  47,  163,  (1905). 

207.  Si-Co.      Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

208.  Si-Ni.      Guertler  and  Tammann Z.  anorg.  Chem.,  49,  93,  (1906). 

209.  (Si-Pd). 

210.  (Si-Pt). 

13.  TIN. 

211.  Sn-Pb.     Stoffel Z.  anorg.  Chem.,  53,  137,  (1907) ;  cf. 

also  Puschin,  C.  B.,  1907,  (2),  2027. 

212.  Sn-Sb.     Williams Z.  anorg.  Chem.,  55,  1,  (1907). 

213.  Sn-Bi.     Stoffel Z.  anorg.  Chem.,  53,  137,  (1907). 

Lepkowski Z.  anorg.  Chem.,  59,  285,  (1908). 

214.  Sn-Cr.     Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 


INVESTIGATION  OF  STRUCTURES. 


335 


215.  Sn-Te.     Fay J.  Am.  Chem.  Soc.,  29,  1265  (1907). 

Pelabon Cr.,  142,  1147,  (1906). 

216.  Sn-Mn.   Williams Z.  anorg.  Chem.,  55,  1,  (1907). 

217.  Sn-Fe.     Isaac  and  Tammann Z.  anorg.  Chem.,  53,  281,  (1907). 

218.  Sn-Co.     Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

Zemczuznyj  and  Belynsky.Z.  anorg.  Chem.,  59,  364,  (1908). 

219.  Sn-Ni.     Guillet Revue  de  Met.,  5,  34,  (1907). 

Voss Z.  anorg.  Chem.,  57,  34,  (1908). 

220.  (Sn-Pd). 

221.  (Sn-Pt). 

/ 

14.   LEAD. 

222.  Pb-Sb.  Gonterman Z.  anorg.  Chem.,  55,  419,  (1907). 

223.  Pb-Bi.  Stoffel Z.  anorg.  Chem.,  53,  137,  (1907). 

224.  Pb-Cr.  Hindrichs Z.  anorg.  Chem.,  59,  414,  (1908). 

225.  Pb-Te.  Fay  and  Gillson Am.  Chem.  J.,  27,  81,  (1902). 

226.  (Pb-Mn). 

227.  Pb-Fe.  Isaac  and  Tammann Z.  anorg.  Chem.,  55,  58,  (1907). 

228.  Pb-Co.  Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

229.  Pb-Ni.  Portevin Rev.  de  Met.,  4,  814,  (1907). 

Voss Z.  anorg.  Chem.,  57,  34,  (1908). 

230.  Pb-Pd.    Ruer Z.  anorg.  Chem.,  52,  345,  (1907). 

231.  Pb-Pt.     Doerinckel Z.  anorg.  Chem.,  54,  333,  (1907). 

15.  ANTIMONY. 

232.  Sb-Bi.     Huttner  and  Tammann. .  .Z.  anorg.  Chem.,  44,  131,  (1905). 

233.  Sb-Cr.     Williams Z.  anorg.  Chem.,  55,  1,  (1907). 

234.  Sb-Te.     Pelabon Cr.,  142,  207,  (1906). 

235.  Sb-Mn.    Williams Z.  anorg.  Chem.,  55,  1,  (1907). 

236.  Sb-Fe.     Kurnakow  and  Konstanti- 

now Z.  anorg.  Chem.,  58,  1,  (1908). 

237.  Sb-Co.     Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

238.  Sb-Ni.     Lossew Z.  anorg.  Chem.,  49,  58,  (1906). 

Kurnakow  andPodkopajew.  .J.  Russ.  Phys.  Chem.  Soc.,  37,  1280, 

(1905). 

239.  (Sb-Pd). 

240.  Sb-Pt.     Friedrich  and  Leroux Metallurgie,  6,  1,  (1909). 


16.  BISMUTH. 

241.  Bi-Cr.     Williams Z.  anorg.  Chem.,  55,  1,  (1907). 

242.  Bi-Te.     Monckemeyer Z.  anorg.  Chem.,  46,  415,  (1905). 

243.  Bi-Mn.   Williams Z.  anorg.  Chem.,  55,  1,  (1907). 

244.  Bi-Fe.     Isaac  and  Tammann Z.  anorg.  Chem.,  55,  58,  (1907). 


336  THE  ELEMENTS   OF   METALLOGRAPHY. 

245.  Bi-Co.     Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

246.  Bi-Ni.     Voss Z.  anorg.  Chem.,  57,  34,  (1908). 

247.  (Bi-Pd). 

248.  (Bi-Ptj. 

17.   CHROMIUM. 

249.  (Cr-Te). 

250.  (Cr-Mn). 

251.  Cr-Fe.     Treitschke Z.  anorg.  Chem.,  55,  402,  (1907). 

252.  Cr-Co.     Lewkonja Z.  anorg.  Chem.,  59,  293,  (1908). 

253.  C--N1.     Voss Z.  anorg.  Chem.,  57,  34,  (1908). 

254.  (Cr-Pd). 

255.  (Cr-Pt). 

18.  TELLURIUM. 

256.  (Te-Mn). 

257.  (Te-Fe). 

258.  (Te-Co). 

259.  (Te-Ni). 

260.  (Te-Pd). 

261.  (Te-Pt). 

19.  MANGANESE. 

262.  Mn-Fe.     Levin  and  Tammann Z.  anorg.  Chem.,  47,  136,  (1905). 

263.  (Mn-Co). 

264.  Mn-Ni.      Zemczuznyj,  Urasow  and 

Rykowskow Z.  anorg.  Chem.,  57,  253,  (1908). 

265.  (Mn-Pd). 

266.  (Mn-Pt). 

20.   IRON. 

267.  Fe-Co.     Guertler  and  Tammann. .  Z.  anorg.  Chem.  45,  205, (1905). 

268.  Fe-Ni.     Guertler  and  Tammann .  .  .  Z,  anorg.  Chem.,  45,  205,  (1905) . 

269.  (Fe-Pd). 

270.  (Fe-Pt). 

21.  COBALT. 

271.  Co-Ni.     Guertler  and  Tammann.  .  .Z.  anorg.  Chem.,  42,  353,  (1904). 

272.  (Co-Pd). 

273.  (Co-Pt). 

22.  NICKEL. 

274.  (Ni-Pd). 

275.  (Ni-Pt). 

23.  PALLADIUM. 

276.  (Pd-Pt). 


INDEX   OF   AUTHORS'    NAMES. 


Abegg  and  Hamburger,  263. 
Adriani,  185,  189 
Alexejew,  151. 
Andrea,  262. 

B. 

Baikow,  247. 
Behrens,  316,  319.  320. 
Benedicks,  227,  229,  230,  234,  328. 
Bijl,  206,  264. 
Boeke,  278,  315. 
Bruni,  165. 

C. 

Charpy,  74.  227,  233,  275,  328. 

—  and  Grenet.  234. 

Chatelier,  Le,  10,  152,  227,  243,  252, 

289,  316,  319.  322,  325. 
Clausius,  249. 


D. 

Day  and  Allen.  Introd.,  8. 
Doerinckel,  159. 
Bolter,  Introd.,  8,  240. 
Dulong  and  Petit,  16. 
Durdin,  186 

F. 

Feussner  and  Lindeck,  252. 

G. 

Gibbs,  25,  36,  165,  267,  285. 

Grube,  89,  103,  195,  303. 

Guertler,  246  et  seq.,  251. 

—  and  Tammann,  190,  192,  219. 

Guthrie,  42. 

Gwyer,  159. 


H. 

Herschkowitsch,  264,  266. 

Heycock  aad  Neville,  70,  215,  296, 

314 

Heyn,  Introd.,  226  et  seq.,  296,  316. 
Heusler,  240. 
Hoff,  van't,  70,  152,  163. 
Holborn  and  Day,  290,  295,  296. 
—  and  Valentiner,  291,  296. 
Hollmann,  192. 
Hiittner  and  Tammann,  11,  20. 

I. 

Isaac  and  Tammann,  206. 

J. 


Juptner,  v.  230. 
Janecke,  277. 


K. 


Kahlbaum  and  Sturm,  242. 
Kamensky,  247. 
Kurnakow,  306. 

—  and  Konstantinow,  223. 

—  and  Stepanow,  94. 

L. 

Laurie,  264. 
Lehmann,  10. 
Levin,  68,  215. 

—  and  Tammann,  180,  297. 
Liebenow,  249,  252. 
Lorentz,  78. 

Lowel,  109. 

Lummer  and  Pringsheim,  291. 

M. 

Maey,  241. 
Mannesmann,  234. 
Martens,  226,  229,  316. 


337 


338 


INDEX   OF   AUTHORS'  NAMES. 


Mathewson,  125,  159,  162. 
Matthiessen,  242. 
-  and  Vogt,  249. 
Meerum  Terwogt,  193. 
Miiller-Erzbach,  262. 
Mylius,  Forster  and  Schone,  228,  266. 

N. 
Nernst,  7,  27,  188,  249,  263,  264. 

—  and  v.  Wartenberg,  295. 
Newton,  12. 

O. 
Osmond,  215,  227,  248,  316  ei  seq., 

320. 
Ostwald,  264. 

P. 

Petrenko,  207. 
Plato,  Introd.,  23. 

R. 

Ramsay,  70. 
Regnault,  16. 
Richards  and  Forbes,  265. 
-and  Wells,  113. 
Rinne,  Introd. 
Roberts-Austen,  227,  306. 

—  and  Kirke  Rose,  215. 
Roland-Gosselin,  72. 
Roscoe,  192. 

Roozeboom,  33,  165,  167,  170,  182, 
187,  192,  200,  201,  207,  218,  227, 
243. 

Rose,  275. 

Ruer,  Introd.,  35,  78,  86,  138,  165, 
174,  193,  295,  314. 


S. 

Sackur,  248,  264,  266. 

Sahmen,  142. 

—  and  v.  Vegesack,  274,  278,  304. 

Saladin  and  Le  Chatelier,  306. 

Schreinemakers,  278. 

Schiiller,  86. 

Shepherd,  207,  215. 

Sorby,  226,  316. 

Spring  and  Romanoff,  152. 

Stoffel,  248,  274. 

T. 

Tammann,  Introd.,  6,  9,  10,  31,  53.  64, 
70,  85,  124,  142,  143,  223,  306, 
313. 

Telden  and  Shenstone,  110. 

Treitschke,  223. 

V. 

v.  Vegesack,  159. 

Vogel,  31,  35,  129,  207,  219,  242,  247, 

294,  319. 
Vogt,  Introd. 


W. 


Wedding,  316. 
Wedekind,  240. 
Williams,  241. 
Wiist,  227,  234. 


Z. 


Zemczuznyj,  219,  226,  299. 

—  Urasow  and  Rykowskow,  186. 


INDEX  OF  SUBJECTS. 


A. 

Addition  resistivity,  250. 
Aluminium-bismuth,  159. 

—  sodium,  159. 

-  thallium,  159. 

—  zinc,  215. 
Antimony-cadmium,  223. 

—  copper,  247. 

—  gold,  129,  166. 

—  lead,  72,  215. 

—  zinc.  226. 

Aqueous  solution  of  common  salt; 
crystallization  of,  38;  vapor  pres- 
sure of,  253. 

Atomic  per  cent,  calculation  of,  from 
weight  per  cent,  70. 

B. 

Ball  microscope,  324. 
Bearing  metals,  275. 
Binary  systems,  34,  37,  et  seq. 
Bismuth-zinc,  150,  151. 
Branch  of  a  curve,  50. 
Brass,  162,  207,  252. 
Break,  43. 

faint,  315. 

Bromine-iodine,  187,  193. 
Bronze,  162,  314. 

C. 

Cadmium-gold,  207. 

—  lead,  243. 

—  magnesium,  187,  195. 
—  mercury,  206,  264. 

—  sodium-mercury,  277. 

-  tin,  243,  248. 

—  zinc,  243. 

Calibration  of  thermo-element,  294. 
Camphoroxine,  d-  and  1-,  189. 
Carbide-carbon,  230. 
arvoxime,  d-  and  ?-,  185. 


Cementite,  228. 

Changes  in  crystalline  state,  143. 
Cobalt-copper,  246. 
Complete     (heterogeneous)     equilib- 
rium, 33,  50,  51,  254,  278,  280. 
Components,  34. 
Compound,     between     isomorphous 

substances,  192,  218. 
melting  to  a  mixture  (emulsion)  of 

two  liquids,  161. 

melting  under  decomposition,  31, 
107;  determination  of  composition 
of  same,  124,  142,  147. 
melting  without  decomposition,  75, 
275;  determination  of  composition 
of  same,  85,  146. 
Compounds,  number  of,  88,  89,  125, 

148. 

Concealed  maximum,  107,  124. 
Concentration     adjustment,     incom- 
plete, 173,  177. 

Concentration-pressure  diagram,  256. 
Concentration-temperature  plane,  48. 
Conductivity,  electrical,  242,  328; 

temperature  coefficient  of,  249. 
Constituents,  independent,  34. 
Convergence  temperature,  13. 
Cooling  curves,  1 1  et  seq.,  42, 117, 164, 
172,  203,  214,  270,  304;  construc- 
tion of  "  idealized,"  306. 
Copper-manganese,  186,  252. 

—  nickel,  192,  243,  252. 

—  palladium,  174,  175. 
-  silver,  215,  247. 

—  thallium,  159. 

—  tin,  162,  314. 

—  zinc,  162,  207,  252. 
Copper  sulphate-water,  257. 
Crystalline  substances,  6. 
Crystallization,  8;  heat  of,  8,  17;  in- 
terval of,  174,  313;  rate  of,  9. 

Cryohydrate,  42. 


339 


340 


INDEX   OF   SUBJECTS. 


Curve,  I-  and  s-,    respectively,    169, 

170. 
Curve  branch,  50. 

D. 

Dilatometrical  methods,  239. 
Dissociation  of  compound  on  heat- 
ing, 79,  104. 

E. 

Electrical  conductivity,  242,  328; 
temperature  coefficient  of,  249. 

Electrical  resistance  furnace,  299. 

Electrolytic  solution  tension,  263. 

Electromotive  force,  264. 

Emery  cloth,  317. 

Emulsion,  159. 

Enantiotropism,  10. 

Envelopment,  135. 

Equilibrium,  25;  actual,  26;  appar- 
ent, 26;  complete,  33,  51,  254, 
280,  281;  heterogeneous,  25;  in- 
complete, 33,  51,  280;  non-vari- 
ant, 283. 

Etching  of  sections,  320;  by  elec- 
tricity, 322. 

Etch-polishing,  320. 

Eutectic  (eutectic  mixture),  42,  59; 
relative  quantity  of,  52;  quan- 
tity of  per  gram-atom,  107; 
structure  of,  62,  67,  84;  ternary, 
270. 

Eutectic  halting  periods,  53,  85,  92, 
310. 

F. 

Ferrite,  229. 

Fields  of  condition,  48,  61;  with  one 

crystalline  variety,  81;  with  two 

crystalline  varieties,  82. 
Freezing  point,  8;  lowering,  38,  76, 

168,  192,  218. 

Furnace,  electrical  resistance,  299. 
Fusion,  7;  apparatus  for,  298;  heat 

of,  8,  20. 
Fusion  curve,  50. 
Fusion  diagram,  47. 

G. 

Galvanometer,  291. 
Gibbs'  principle,  165. 


Glauber's  salt,  107. 
Gold-copper,  215,  243. 

—  nickel,  215. 

—  palladium,  174,  177. 

—  silver,  243. 

—  tin,  246,  247. 

—  zinc,  219. 

Graphical  representation,  3. 

Graphite,  231. 

Grinding,  317;  in  relief,  320. 

H. 

Halting  point,  18. 

Halting  period,  53,  85,  92,  124,  310. 

Hardening  carbon,  230,  231. 

Hardening  of  steel,  237. 

Hardness,  317,  328. 

Heat  of  formation,  266. 

Heat  of  fusion,  8,  20,  21. 

Heat  of  transformation,  11,  21. 

Heating  curves,  11  et  seq.,  305;  con- 
struction of  "idealized"  306. 

Homogeneity,  treatment  for,  182. 

Horizontal  course  of  the  fusion  curve 
through  a  finite  concentration 
interval,  189. 

Horizontal  inflexional  tangent  to  the 
fusion  curve,  166,  186. 

Horizontal  tangent  to  the  fusion 
curve,  166,  182,  185,  187,  207, 
211. 

I. 

Immiscibility,  complete,  37,  213;  in 
crystalline  state,  38,  69,  149,  269. 

Impassable  line,  276. 

Incomplete  (heterogeneous)  equilib- 
rium, 33,  50,  51,  278. 

Incomplete  progress  of  decomposi- 
tion, 134. 

Independent  constituents,  34. 

Inflexional  tangent,  horizontal  to  the 
fusion  curve,  166,  186. 

Inoculation,  9,  10,  305. 

Iron-carbon,  162,  226  et  seq. 

—  cobalt,  190. 

—  gold,  207. 

—  manganese,  180 

—  nickel,  240. 
Isodimorphism,  201,  219. 
Isomorphism,  complete  or  unbroken, 

163,  277;  limited,  201,  219. 


INDEX   OF  SUBJECTS. 


341 


L. 

Lamellar  structure  of  eutectic,  62,  67. 
Law  of  cooling,  Newton's,  12. 
Z-curve,  169. 
Lead-cadmium,  243. 

—  gold,  31. 

—  tin,  243,  248. 

—  tin  -bismuth,  275. 

—  zinc,  152. 
Lever  relation,  54. 

M. 

Magnesium-bismuth,  103. 

—  silver,  219. 

—  sodium,  159. 

—  tin,  89. 

Magnetic  properties,  240. 

Manganese-nickel,  186. 

Martensite,  229. 

Maximum,  concealed,  107,  124,  219; 
upon  the  fusion  curve,  78,  166, 
182,  188,  193,  218. 

Maximum-minimum  upon  the  fusion 
curve,  166,  186. 

Melting  point,  7;  lowering,  38,  76, 
168,  192,  218;  of  a  compound 
fusing  under  decomposition,  32. 

Metal  mixture,  Rose's,  275. 

Microscope  according  to  Le  Chate- 
lier,  325. 

Microscopical  investigation  of  sec- 
tions, 323. 

Millivoltmeter,  291. 

Minimum  upon  the  fusion  curve,  166, 
185,  188. 

Miscibility,  37;  complete,  in  liquid 
state,  38,  132,  196,  269,  277; 
incomplete,  in  liquid  state,  149, 
222;  complete,  in  crystalline 
state,  162,  222,  277;  incomplete, 
in  crystalline  state,  196,  222. 

N. 

Nickel-silicon,  219. 
Nickel  steel,  240. 
Non-variant  system,  283. 

O. 

One  component  systems,  3  et  seq.,  34. 
Open    maximum    upon    the    fusion 
curve,  78,  166,  182,  188,  193,  218. 
Optical  methods,  240. 


P. 

Palladium-silver,  174,  176. 

Parkes  process,  37. 

Pearlite,  230. 

Phase  rule,  36,  278. 

Phases,     25;    arrangement    of,    27; 

quantity  of,  27. 
Photography,  325. 
Pig  iron,  236. 
Polishing,  316. 
Polymorphous    transformations,    10, 

143,  190,  215. 

Potassium-sodium-mercury,  277. 
Pressure,  influence  of,  7,  281. 
Principle  of  Van't  Hoff  and  Le  Chate- 

lier,  152. 
Pyrometers,  289;  self-registering,  306. 

Q. 

Quantitative  relations  on  disinte- 
gration into  two  phases,  54. 

Quantity  of  eutectic  per  gram-atom, 
107. 

Quantity,  relative,  of  eutectic,  52. 

Quaternary  alloys,  36. 

Quenching,  147. 

R. 

Rate  of  cooling,  13. 

Reactions  in  the  crystalline  medium, 

143. 

Relative  quantity  of  eutectic,  52. 
Relief,  grinding  in,  320. 
Relief-polishing,  320. 
Residues,  analysis  of,  266. 
Resistance  furnace,  electrical,  299. 
Reversible  processes,  10. 

S. 

s-curve,  170. 

Section,  preparation  of,  316. 

Segregation,  138,  317. 

Self-registering  pyrometer,  306. 

Silver-zinc,  207. 

Sodium-bismuth,  125. 

—  zinc,  162. 

Sodium  chloride-water,  38,  253. 

Sodium  sulphate,  107. 

molybdate-tungstate,  278. 

Solid,  6. 


342 


INDEX  OF  SUBJECTS. 


Solidification,  temperature  of,  38. 

Solid  solution,  163. 

Solubility,  mutual,  and  state  of  aggre- 
gation, 37;  of  a  component,  263. 

Solubility  and  stability,  109,  122. 

Solubility  curve,  of  two  liquids,  150; 
of  two  crystalline  varieties,  197. 

Solubility  determination,  method  of, 
238. 

Solution,  solid,  163. 

Solution  tension,  electrolytic,  263. 

Stability,  incomplete,  223. 

Stability  and  solubility,  109,  122. 

Steel,  237. 

Structure,  abnormal,  137,  141,  284; 
development  of,  319;  investiga- 
tion of,  316,  323;  of  sections, 
64,  65,  284. 

Supercooled  conditions,  123,  223  et 
seq. 

Supercooling,  9. 

Superheating,  8. 

Systems,  25;  homogeneous  and  hete- 
rogeneous, respectively,  25;  non- 
variant,  283;  one  component,  3 
et  seq.,  34:  two  component,  or 
binary,  34,  37  et  seq.;  three  com- 
ponent, or  ternary,  34,  267  et  seq. 

T. 

Tangent,  horizontal  to  the  fusion 
curve,  166,  182,  185,  187,  207, 
211. 

Tarnishing  of  sections  in  air,  65,  322. 

Temperature,  measurement  of,  289. 

Temperature  coefficient  of  electrical 
conductivity,  249. 


Temperature  of  free  ends  of  thermo- 
element, 293. 

Tempering,  234,  238. 

Thallium-zinc,  159. 

Thermal  analysis,  Introd. 

Thermal  investigation,  289. 

Thermo-element,  289. 

Three  component  systems,  34,  267 
et  seq. 

Transformation,  of  a  pure  substance, 
6;  polymorphous,  10,  143,  190, 
215;  reversible  (enantiotropic) 
10. 

Transformation  temperature  (transi- 
tion temperature),  11. 

Triangular  coordinates,  267. 

Two  component  systems,  34,  37  et 
seq. 

Type  I  (of  mixed  crystals),  167. 

—  la,  187,  207. 

—  II,  182. 

—  Ill,  185,  212. 

—  IV,  200,  201  et  seq. 

—  V,  200,  208  et  seq. 

V. 

Vapor  pressure,  252;  lowering,  253. 
Vertical  illuminator,  65,  324. 
Voltmeter,  291. 
Volume,  specific,  241. 
Volume-pressure  diagram,  255. 

W. 

Wrought  iron,  237. 

Z. 

Zinc-tin,  243. 


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